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6
Working with
Money
Carmen and Adriana are farmers who sell products in bulk at the
market.
A. Many businesses buy supplies in bulk. Why do you think they
do this?
e.g., Supplies usually cost less in bulk. Businesses also use a lot of supplies, so it makes sense to buy a lot at one time.
B. What would be an advantage and a disadvantage to buying
things in bulk?
e.g., You probably get a lower price, but it’s harder to estimate how much you’re spending if the price depends on the exact quantity you take.
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6.1
calculating Unit Price
try these
i) $15.90 ÷ 5 = $ 3.18
ii) ($12.00 + $9.00 + $21.00) ÷ 4 = $ 10.50
unit price
the amount of
money charged
for a unit of an
item
Heidi sells cleaning products in bulk at her store. She puts the
liquid in large containers and customers can fill their own bottles.
How should Heidi display the unit price for a cleaner that sells for
$115 for 25 L?
1
Calculate the price for each quantity.
Price per litre: $115 ÷ 25 L = $ 4.60 /L
Price per 500 mL: $ 4.60 /L ÷ 2 = $ 2.30
Hint
1000 mL = 1 L
Price per 100 mL: $ 4.60 /L ÷
2
10
/500 mL
= $ 0.46 /100 mL
Should Heidi display the price per litre, per 500 mL, or
per 100 mL? Why?
e.g., I think she should display the price per 500 mL because that’s what most people will buy and it doesn’t look as expensive as the price per litre.
$1.99/kg
Reflecting
When might it be
useful to know the
unit price of items?
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Example
Rama advertises bananas for $1.99 per kilogram. Is this more or
less than 59¢ a pound?
Solution
A. What relationship can you use to determine the unit cost
per pound of the bananas?
1 pound =∙ 0.45 kg
$ 1.99 /kg × 0.45 kg/lb =∙ $ 0.8955 /lb
B. Is $1.99/kg more or less than 59¢ a pound? more
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:42:47 PM
Practice
1. Calculate each unit price.
a) 12 eggs for $3.24
$ 0.27 per egg
c) $23.90 for 1 kg of pecans
$ 2.39 /100 g
$23.90  10 = $2.39
$3.24  12 = $0.27
b) $35.16 for 40 L of gas
$ 0.879 /L or 87.9 ¢/L
d) $23.90 for 1 kg of pecans
about $ 10.76 per pound
$35.16  40 L = $0.879
$23.90 x 0.45 kg/lb = $10.76
2. Raymond needs to order crushed rock for a courtyard.
What is the cost of 4.5 t at $12.50 per tonne?
e.g., 4.5 t x $12.50/t = $56.25
The crushed rock will cost $56.25.
3. One brand of salsa is $5.95 for 650 mL and another is
$4.10 for 350 mL.
a) What is the price per millilitre for each brand?
650 mL: $5.95  650 mL = $0.009…/mL
$5.95
$4.10
350 mL: $4.10  350 mL = $0.011…/mL
b) What is the price per 100 mL for each brand?
650 mL: $0.009… x 100 = $0.91 per 100 mL
350 mL: $0.011… x 100 = $1.17 per 100 mL
4. Lise labels her meat prices per pound. Jordan labels his meat
prices per kilogram. Calculate the equivalent unit price for
each.
Rib steak
$8.80/lb
$ 19.45 /kg
Sirloin roast
$ 3.43 /lb
Hint
1 kg =∙ 2.21 lb
$7.59/kg
5. Tanya found these prices for tomato
juice:
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A: 1.89 L for $3.99 B: 750 mL for
$2.99 C: 250 mL for 89¢
Figure Number
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Which size sells for the lowest unit
price?
Company
e.g., $3.99 = A
$2.99 =Technical
B
Pass
0.75 L
1 L $0.89 = C
1st Pass
0.25 L
1 L
B costs $3.99/L Not Approved
C costs $3.56/L
1.89 L
1 L A costs $2.11/L Approved
The 1.89 L size has the lowest unit price.
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6.2
Determining the Best Buy
try these
i) $52 ÷ 5  $ 10.40
iii) $468 ÷ 18  $ 26.00
ii) $6.25 ÷ 12  $ 0.52
iv) $899 ÷ 4  $ 224.75
Indie is an interior designer. She is choosing fabric for curtains for
her client’s living room.
• Linen at $38.25 for 3 yards
• Cotton at $60.00 for 8 yards
Which fabric has the lower unit price?
1
What is the price per yard for each fabric?
Linen: $38.25 ÷ 3 yards = $ 12.75 per yard
Cotton: $ 60.00 ÷
8
yards = $ 7.50 per yard
2
Which fabric has the lower unit price? cotton
3
What other factors might Indie consider when buying fabric?
e.g., quality, care, look, amount she needs, the distance she must drive to a store
Example
Osmani is a tour operator. He offers two types of tours of Banff.
• Deluxe Tour offers 90 min of sightseeing for $36.
• Supreme Tour offers 4 h of sightseeing for $84.
Which tour offers a better price per hour?
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Hint
Remember to
compare units that
are the same.
Reflecting
Why is the lower
unit price sometimes
not the best option?
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Solution
A. Deluxe Tour unit price: 90 min =
$36 ÷ 1.5 h = $ 24 /h
Supreme Tour unit price: $84 ÷
1.5
h
4
h=$
21
/h
B. Which tour offers the better price per hour?
Supreme, because they charge $3 less per hour
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:42:48 PM
Practice
1. Determine the lower unit price.
a) 2000 nails for $54.99 or 5000 nails for $119.99
$54.99  2000 =· $0.03/nail
$119.99  5000 =· $0.02/nail ←lower
b) Swiss cheese at $4.59 for 170 g or havarti at $2.29/100 g
e.g., Swiss: $4.59  170 g x 100 = $2.70/100 g
Havarti: $2.29/100 g ←lower
c) Yogurt: 650 g for $2.99 or 800 g for $5.59
e.g., $2.99  650 g x 100 = $0.46 ←lower
$5.59  800 g x 100 = $0.70
d) Roast chicken at $2.29/100 g or ham at $3.29/175 g
e.g., Ham: $3.29  175 g x 100 = $1.88/100 g ←lower
Roast chicken: $2.29/100 g
e) 3.78 L of house paint for $39.95 or 237 mL for $6.49
e.g., $39.95  3.78 L = $10.57/L ←lower
$6.49  237 mL x 1000 = $27.38/L
2. Candace needs to replace two of her winter tires. She finds
the following prices.
• Main Street Tire: 1 tire for $82.15
• Tom’s Automotive Shop: 2 tires for $140.56
Which store offers the better price for Candace?
e.g., $140.56  2 = $70.28 per tire
Tom’s Automotive Shop offers the better price.
3. Henry needs a small amount of paint for a bathroom wall. He
can pay either $32.97 for 3.8 L of paint or $15.49 for 950 mL.
Which would be the better buy? Explain your thinking.
$32.97  3800 mL =· $0.01/mL
$15.49  950 mL =· $0.02/mL
e.g., The 3.8 L can has the better unit price, but Henry needs
only a small amount of paint. AW10
So he should buy 950 mL.
0-17-650271-8
Figure Number
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Company
Technical
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4. Carol-Hui is buying orange juice. Which has the better unit
price?
• Concentrated orange juice: $1.85 for 355 mL; mix with
3 cans (355 mL each) of water to serve
• Ready-to-serve orange juice: $2.99 for 1.89 L
e.g., Concentrated: 355 mL x 4 = 1420 mL or 1.42 L $1.85  1.42L =· $1.30/L
Ready-to-serve: $2.99  1.89 L =· $1.58/L
The concentrated orange juice has a better unit price.
5. Vince wants to hire a contractor to finish his basement.
He got quotes from two companies.
Company
name
Experience
Customer
satisfaction
Hourly
rate
Estimated
time
Cost of
supplies
Frank
& Sons
Contractors
well-known
and
experienced
98%
$70/h
24 h
$2000
Design and
Build Team
new to the
business
79%
$50/h
28 h
$2200
a) What would each company charge in total?
Frank &Sons Contractors: $70 x 24 h +2000 = $3680
Design and Build Team: $50 x 28 h +2200 = $3600
b) Which would be the better option? Explain your thinking.
e.g., Frank &Sons Contractors would be the better option.
They are well-known and experienced and cost only an
extra $80.
6. Which is the better unit price?
a) pop at $1.99 for 2 L or 55¢ for 355 mL
e.g., $1.99  2 L =· $0.99/L
$0.55  0.355 L =· $1.55/L
The 2 L pop costs less per litre.
b) beef at $4.99/lb or $8.50/kg
e.g., 1 kg =· 2.21 lb
$4.99/lb x 2.21 lb/kg =· $11.03/kg
The beef at $8.50/kg costs less.
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7. Jayden is a flooring installer. He provides the
information below for a client trying to decide
what kind of flooring to use.
Type of
flooring
Warranty
Unit price
Amount
needed
ceramic tile
lifetime
$6.36/tile
120 tiles
laminate tile
10 years
$54.01/box
13 boxes
a) Calculate the total price for each type
of flooring.
Ceramic: 120 tiles x $6.36/tile = $763.20
Laminate: 13 boxes x $54.01/box = $702.13
b) Which type of flooring do you think the client should
choose? Explain your thinking.
e.g., The ceramic tiles are not much more expensive than laminate tiles, so the client should choose the ceramic tiles because they last longer.
8. Corey buys his engine oil online. Which is a better unit price?
3 US gallons for $35.95 or 5 L for $29.95
e.g., 1 US gal =· 3.79 L, so 3 US gal =· 11.37 L
Hint
Remember to use
the same units.
Use the charts
inside the back
cover.
$35.95  11.37 L =· $3.16/L
$29.95  5 L = $5.99/L
3 US gallons is a better unit price.
9. a) What are some factors to consider when looking for the
best buy?
e.g., quality, quantity, unit price, discounts, convenience of place to buy, labour costs for different materials, time
b) Is the cheaper option always the best buy? Explain your
thinking.
No. e.g., Sometimes quality counts for more than quantity. Also, if you buy too much of something to get a better unit price, things would go to waste.
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6.3
calculating Discounts and increases
try these
i) 25% of $800  $
ii) 80% of $1500  $ 1200
200
Hilda needs to make room for the summer line in her clothing
store. She needs to calculate sale prices for her existing stock
and set prices for her new arrivals.
1
How much will she charge for an $80 pair of jeans with a
discount of 25%?
Discount: $80 × 0.25 = $ 20
Sale price: $
2
80
−$
20 = $
60
Hilda bought a new line of jeans for $42.50/pair. She will mark
them up by 48%. What will she charge for the jeans?
Mark up: $42.50 × 0.48 = $ 20.40
Ticket price: $ 42.50 + $ 20.40 = $ 62.90
3
What profit will Hilda make for each pair of jeans sold?
e.g., $62.90 – $42.50 = $20.40
Hilda will make $ 20.40 in profit for each pair of jeans sold.
Example 1
Owen is offering a discount on an apartment of
1
5
off the first
month’s rent of $1200. What will the first month’s rent be?
Solution 1
Calculate the cost by first calculating the discount amount.
Discount:
$1200 ×
1
5
First month’s rent: $1200  $ 240
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= $ 240
= $ 960
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4/20/10 1:42:50 PM
Solution 2
Calculate the cost in one step.
1
(or 20%) off means 45 (or 80%) of the original price.
5
First month’s rent: $1200 ×
Reflecting
Which do you
prefer, Solution 1 or
Solution 2? Why?
0.80 = $ 960
Example 2
Ben bought a house for $265 000. After one year, it increased in
value by 4%. What was the value of Ben’s house after one year?
Solution
$265 000 × (1.00 +
0.04 ) = $265 000 ×
Hint
If you include 1.00
in the equation,
you can skip the
step where you
add the increase to
the original price.
1.04
= $ 275 600
Example 3
Aida paid $693 wholesale for mirrors that sell for $990 retail.
What discount was she given?
Solution
A. What percent of the original price is the sale price?
sale price
= percent of original price
original price
693 =
990
0.7
, or
Reflecting
What could be a
general rule for
figuring out an
increased price in a
single calculation?
%
70
B. What is the discount?
100%  70 % = 30
%
Practice
1. Complete the chart for these sales offers.
Item
Original price
Discount
computer
$679.99
15%
newspaper ad
$500.00
snowboard
$455.95
60%
shoes
$72.95
20%
1
4
off
Copyright © 2011 by Nelson Education Ltd.
New price
$577.99
$375.00
$182.38
$58.36
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2. Seo Ho is opening a new restaurant and needs to buy plates.
• Supplier 1: 300 plates for $3400
• Supplier 2: 300 plates for $4000 and a 10% discount
Which supplier is offering the better price?
e.g., $4000 x 0.90 = $3600
Supplier 1 is offering the better price.
3. Complete the chart for these salary increases.
Name
Original salary
Percent increase
Carrie
$52 000
7%
Gerry
$44 500
2%
Sandra
$108 200
3.5%
Andrew
$82 300
4.5%
New salary
$55 640
$45 390
$111 987
$86 003.50
4. In one year, prices in Canada’s housing market increased
by 5.2%. If a house sold for $335 576 at the beginning of
that year, what could it sell for at the end of that year?
e.g., $335 576 x 1.052 =· $353 026
The house could sell for $353 026.
5. Alysha restored an old motorcycle. She paid $26 000, spent
$3500 on repairs, and sold it for $37 000. What percent profit
did she make?
e.g., $26 000 +$3 500 = $29 500
$37 000 – $29 500 = $7500
$7 500  $29 500 x 100 = 25.423…%
Alysha made about 25% in profit.
6. Zoe is opening an organic greenhouse. She paid $130
wholesale for gardening tools worth $200 retail. What was
the percent discount for the tools she bought?
e.g., 130  200 = 0.65
1.00 – 0.65 = 0.35
The discount was 35%.
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6.4
Analyzing Sales Promotions
try these
i) 2.5 × $1.95  $
iii) 80% of $1200 = $
4.88
ii) 4 × $9.50 + $20  $
58
960
iv) 20% off $1200  $ 960
Jack is buying plywood for his cabinetmaking business. Two
lumberyards sell 34 inch oak plywood for $79.98 a sheet, but they
offer different promotions.
• Promotion 1: spend more than $500 and get $100 off
• Promotion 2: 15% discount off entire purchase
Which promotion is better for Jack if he needs 8 sheets?
if he needs 16 sheets?
1
If Jack needs 8 sheets of plywood to make new cabinets,
which promotion will save him the most money?
$79.98 × 8 sheets = $ 639.84
Promotion 1: $ 639.84 — $ 100 = $ 539.84
Promotion 2: $ 639.84 × 0.85
Promotion
8 sheets.
2
1
= $ 543.86
saves Jack the most money if he buys
If Jack wanted to buy 16 sheets of plywood, which option
would save him the most money?
$79.98 × 16 sheets = $ 1279.68
Promotion 1: $ 1279.68 — $ 100
Promotion 2: $ 1279.68 × 0.85
Promotion
16 sheets.
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= $ 1179.68
= $ 1087.73
saves Jack the most money if he buys
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:42:52 PM
Example
Kristin is buying six watches as gifts for her friends. The store has
two promotions to choose from for watches with a regular price of
$12 each.
• The real deal: buy one, get one half price
1
• The big discount: 3 off the purchase
Which promotion should Kristin choose?
Solution
Calculate the price for each promotion.
The real deal: $12 × 3 + $ 6
×3=$
The big discount: $12 × 6 
54
× 6) = $
48
Kristin should choose the big discount.
Practice
1. Nikki needs eight new sets of linens for her massage therapy Reflecting
What other types of
business. She checks out the sales at two different stores.
sales promotions
• Bedding & More: buy 1 get 1 free; regular price $32.50/set have you seen?
• Lydia’s Linens: 40% off regular price of $26.49
a) How much do eight sets of linens cost at each store?
e.g., Bedding & More: $32.50 x 4 = $130.00
-8
er
1
($12
3
C06-F11-AW10.eps
Lydia’s Linens: $26.49 x 0.60 = $15.89 $15.89 x 8 = $127.15
AW10
2nd Pass
0-17-650271-8
b) Which store offers the better
price? Lydia’s Linens
Figure Number
C06-F11-AW10.eps
Company
d
2. Allison is a freelance graphic Technical
designer. She needs to
Pass
2nd Pass
buy a new computer for her business.
Two stores
Approved
offer promotions on the same computer.
Not Approved
• $2899 with a discount of 20%
• $2779 with a $250 mail-in rebate
Which is the better price?
e.g., $2899 x 0.80 = $2319.20
$2779 – $250 = $2529.00
The 20% discount on $2899 is a better price.
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3. Troy is going to a technical school in the fall and needs to rent
an apartment. He finds two apartments that he likes.
• Apt. 1: $700/month +
1
2
month’s rent for a damage deposit
• Apt. 2: $775/month with the first month free
a) If Troy needs the apartment for 12 months, which
apartment would be less expensive?
Apartment 1: $700/month x 12 months +$350 = $8750
Apartment 2: $775/month x 11 months = $8525
Apartment 2 would be less expensive for 12 months.
b) If Troy needed the apartment for 24 months, which
apartment would be less expensive?
Apartment 1: $700/month x 24 months +$350 = $17 150
Apartment 2: $775/month x 23 months = $17 825
Apartment 1 would be less expensive for 24 months.
4. Ngor needs to rent a vehicle to drive from Invermere, British
Columbia, to Lethbridge, Alberta, and back. The total
distance for the round trip is 607 km and will take two days.
• RentCar: $45.99/day with unlimited mileage
• Car Bud: $15.85/day plus $0.12/km
a) Which option seems less expensive, without calculating
unit prices? Why?
e.g., Car Bud seems cheaper because the rental fee is less.
b) Which option is best for Ngor’s situation?
RentCar: $45.99/day x 2 days = $91.98
Car Bud: ($15.85/day x 2 days) +($0.12/km x 607 km) = $31.70 +$72.84 = $104.54
RentCar would be less expensive for Ngor.
c) If Ngor’s trip only took one day, which option would be
less expensive?
RentCar: $45.99
Car Bud: $15.85 +($0.12/km x 607 km) = $15.85 +$72.84 = $88.69
RentCar would be less expensive.
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6.5
Solving a Money Puzzle
Stephen wants to purchase a new hybrid car.
• The base price of the car is $27 800.
• He would like to purchase the premium package with solar
panels for $3835, leather seats for $1890, and a remote car
starter for $632.
• GST is 5% of the total purchase price.
Stephen has gone to three different dealerships.
Each dealership has a different promotion.
• Dalia’s Dealership: dealer pays the
GST (5%) on the purchase price
• Dan’s Dealership: manufacturer offers
a 1% price reduction and a rebate of $2000
• Drake’s Dealership: dealer offers a
1.5% price reduction and $1500 in
fuel vouchers
A. Which dealership offers the lowest price?
e.g., Total price: $27 800 +$3 835 +$1 890 +$632 = $34 157
Price, including GST: $34 157 x 1.05 = $35 864.85
Dalia’s: $34 157
Dan’s: $34 157 x 99% = $33 815.43
$33 815.43 + ($33 815.43 x 5%) = $35 506.20
$35 506.20 – $2000 = $33 506.20
Drake’s: $34 157 – ($34 157 x 1.5%) = $33 644.65 $33 644.65 x 1.05 = $35 326.88
$35 326.88 – $1500 = $33 826.88
Dan’s Dealership has the lowest total price.
B. Which offer is best for the dealership? Why?
e.g., Dan’s offer is also best for the dealership because the manufacturer is offering the promotion, not the dealership.
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6.6
currency exchange
try these
rate of exchange
the amount
that money is
worth from one
currency to
another. This
varies daily.
i) 1.987 × $20  $ 39.74
iii) $2000 × 0.9671 = $ 1934.20
ii) $500 × 0.6789  $ 339.45
iv) $89 × 0.146  $ 12.99
Trevor will be travelling to the WorldSkills Competition in London,
England. He needs to convert his Canadian dollars (C$) to British
pounds (£). To find the latest rate of exchange, Trevor checks an
online currency converter.
1
For every C$1, Trevor would receive £0.607. How many
British pounds (£) will he get for C$500?
Amount in C$ × exchange rate = amount in £
C$ 500 × £0.607/C$ =∙ £ 303.50
2
If Trevor wants to take £500, how much will that cost in
Canadian dollars?
C$ × £0.607/C$ =∙ £500
£500 ÷ £0.607/C$ = C$ 823.72
Currency exchange rates change every day. Here is a sample.
Hint
To use the
currency chart,
find the column
for the currency
you’re starting
with. Then
go down that
column to find the
exchange rate for
the currency you
want to convert to.
172
06C06.indd 172
Canadian
dollar ($)
US
dollar
($)
Euro
(€)
British
pound
(£)
Japanese
yen (¥)
Mexican
peso ($)
Chinese
yuan (¥)
Canadian
dollar ($)
1.000
1.035
1.482
1.650
0.011
0.081
0.152
US dollar
($)
0.967
1.000
1.431
1.594
0.012
0.078
0.146
Euro (€)
0.676
0.699
1.000
1.114
0.008
0.055
0.102
British
pound (£)
0.607
0.627
0.898
1.000
0.007
0.049
0.092
Japanese
yen (¥)
90.198
93.185
133.388
148.55
1.000
7.303
13.638
Mexican
peso ($)
12.340
12.760
18.265
20.341
0.137
1.000
1.867
Chinese
yuan (¥)
6.602
6.833
9.781
10.893
0.073
0.536
1.000
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:42:57 PM
Example 1
Danielle wants to travel to buy textiles. She has $2000 Canadian.
What is that amount worth in Chinese yuan (¥), Japanese yen (¥),
and euros (€)?
Solution
A. What is C$2000 worth in Chinese yuan (CN¥)?
e.g., C$1 =∙ ¥ 6.602
C$2000 × ¥ 6.602 /C$ =∙ CN¥ 13 204
Hint
You may use the
exchange rates
from the chart or
look up current
exchange rates.
Reflecting
Why would it be
important to know
the exchange rate
of the country you
are travelling to
before you get
there?
B. What is C$2000 worth in Japanese yen (JP¥)?
e.g., C$2000 × ¥ 90.198 /C$ =∙ JP¥ 180 396
C. What is C$2000 worth in euros?
e.g., C$2000 × € 0.676 /C$ =∙ € 1352
Example 2
Danielle has €420 left after travelling to Europe
and wants to go to Mexico. What is €420 worth
in Mexican pesos (MX$)?
Solution For example:
€1 =∙ MX$ 18.265
€420 × MX$ 18.265 /€ =∙ MX$ 7671.30
Practice
1. Determine the equivalent for each exchange. For example:
Starting
currency
Canadian
dollar
Euro
Mexican peso
Japanese yen
US dollar
British pound
Chinese yuan
Amount
Convert to
Exchange
rate
C$1
US dollars
0.967
€1
Canadian dollars
1.482
MX$1
British pounds
0.049
JP¥1
Chinese yuan
0.073
US$1Apprenticeship
Mexican pesos
& Workplace12.760
GR 10
£1 0-17-650271-8
Japanese yen
148.55
CN¥1FN
Euros C06-F16-AW10WB
0.102
CO
Technical
Copyright © 2011 by Nelson Education
Pass Ltd.
Approved
Not Approved
06C06.indd 173
Amount
US$0.97
C$1.48
£0.05
CN¥ 0.07
MX$12.76
JP¥ 148.55
€0.10
CrowleArt Group
Deborah Crowle
Chapter 6 Working with Money
1st pass
173
4/20/10 1:42:58 PM
2. Pierre is going on a work exchange program in Europe.
He can fly from Paris, France, to Athens, Greece, for €187.
What would his flight cost in Canadian dollars?
e.g., €1 =· C$1.482
€187 x $1.482/€ =· C$277.13
The flight would cost C$277.13.
3. Determine the equivalent for each exchange. For example:
Starting
currency
Amount
Convert to
Exchange
rate
Canadian
dollars
C$300
US dollars
0.967
US$290.10
Euros
€689
Canadian dollars
Mexican pesos
MX $35
British pounds
Japanese yen
JP¥2700
Chinese yuan
US dollars
US $25
Mexican pesos
British pounds
£540
Japanese yen
Chinese yuan
CN¥99
Euros
1.482
0.049
0.073
12.760
148.55
0.102
C$1021.10
£1.72
CN¥ 197.10
MX$319.00
JP¥ 80 217.00
€10.10
Amount
4. Sebastian is shopping in Spain and wonders if a sweater
priced at €45 is reasonable compared with a similar $30
sweater he bought in Nelson, British Columbia. Compare
the prices.
e.g., €1 =· C$1.482
€45 x C$1.482/€ =· C$66.69
The sweater in Spain is more than twice the price of the Canadian sweater.
5. Amanda is travelling to Haiti to help build a health care clinic.
She is taking $500 Canadian to exchange for Haitian gourdes.
How much is C$500 worth in Haitian gourdes (HTG)?
C$1 =∙ 37.5858 gourdes (HTG)
e.g., C$500 x 37.5858 gourdes/C$ =· 18 792.9 gourdes
6. Tessa is comparing the price of books online. At a Canadian
store, one book costs C$20.49. At an American store, the
same book costs US$18.95. Which price is less?
e.g., C$20.49 x C$0.967/US$ = US$19.81
The price at the American store is less.
174
06C06.indd 174
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:42:58 PM
7. On a trip to California, Tara spent the amounts below. Express
these prices in Canadian dollars. For example: (Note that current exchange rate
may be used.)
Breakfast
US$12.82 × 1.0684 =∙ C$ 13.70
Dinner
Transportation
Clothing
US$75.88 × 1.0684 =∙ C$ 81.07
US$642.25 × 1.0684 =∙ C$ 686.18
US$120.79 × 1.0684 =∙ C$ 129.05
8. Julia bought oranges for €1.99 per kilogram at a market in
Germany. She wondered how this compared to the price of
oranges in Red Deer, Alberta, at 79¢ per pound.
a) What is the price of €1.99/kg in euros per pound?
e.g., 1 kg =· 2.21 lb
€1.99/kg  2.21 lb/kg = €0.900…/lb
b) What is the price in Canadian dollars per pound?
e.g., €1 =· $1.482
€0.9004/lb x $1.482/€ = $1.334.../lb
c) Where are the oranges less expensive?
Alberta
9. Elijah and his family travelled to China. Before they left, they
exchanged $3600 Canadian for Chinese yuan.
a) What is the value of C$3600 in yuan (CN¥)?
e.g., C$1 =· CN¥6.602
$3600 x ¥6.602/C$ =· CN¥23 767.20
b) While in China, they spent CN¥20 419. They exchanged
the remainder back to C$. What is the value in C$?
e.g., CN¥23 767.20 – CN¥20 419 = CN¥3 348.20
CN¥1 =· C$0.152
CN¥3348.20 x C$0.152/CN¥ = C$508.93
They had $508.93 Canadian.
10. Marco is a landscape gardener. He is travelling
to learn more about English and Japanese
gardens. When he left England, he had £350.
What is this worth in Japanese yen?
e.g., £1 =· JP¥148.55
£350 x ¥148.55/£ =· JP¥51 992.50
Copyright © 2011 by Nelson Education Ltd.
06C06.indd 175
Chapter 6 Working with Money
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6.7
estimating currency exchange
try these
i) 0.5 × $2200  $
iii) 1.5 × $400 = $
1100
ii) 0.1 × $4200  $ 420
iv) 2.5 × $20  $
600
50
Akai needs to create budgets for her business trips. What
numbers can she use to estimate without using a calculator?
Hint
To estimate the
value of Canadian
dollars in yen,
multiply by 100.
To estimate an
amount in yen in
C$, divide by 100.
1
Akai is travelling from Canada to Japan. What would be a
good estimate for the exchange rate of Canadian dollars to
Japanese yen if C$1 =∙ JP¥90.198?
C$1 = about JP¥ e.g., 100 2
Akai is travelling from Canada to Scotland. What would be a
good estimate for the exchange rate of C$ to British pounds if
C$1 =∙ £0.607?
1
C$1 = about £ e.g., 2
Example
Bakana is a flight attendant
for a British airline. She
has £300. How can she
estimate this amount in
Canadian dollars?
Hint
You can use
mental math when
calculating
300 × 1.5. Just
take half of 300
and add it to 300.
Solution
1
£1 is about C$1 2 .
So £300 is about
C$300 + C$ 150 ,
which is about
C$ 450
Reflecting
When might it be
useful to estimate
an amount in a
different currency?
176
06C06.indd 176
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:43:03 PM
Practice
1. Show a reasonable estimate for each exchange rate. For example:
Starting
currency
Amount
Convert to
Exchange
rate
7.245
Estimate
7 R
Canadian dollars
C$1
South African rand
Canadian dollars
C$1
Mexican pesos
Canadian dollars
C$1
Euros
0.676
€2
Mexican pesos
MX$1
Canadian dollars
0.081
1
C$ 10
Thai baht
1 THB
Canadian dollars
0.0322
C$0.03
Chinese yuan
CN¥1
Canadian dollars
0.152
C$0.15
12.34
MX$12
Hint
You may look up
current exchange
rates online.
1
2. Hannah is taking a pastry chef program in France. The tuition
is €4000. About how much is the tuition in Canadian dollars?
e.g., €1 is about C$1.5.
4000 +2000 = 6000
So the tuition is about C$6000.
3. Sue would like to place an order for a shipment of shirts for
her retail store. The shipment costs about 5000 Mexican
pesos. About how much would the shipment be worth in
Canadian dollars? Explain how you estimated.
e.g., 1 peso is worth about 10¢, so I can just divide by 10.
MX$5000  10 =· C$500
The shipment would be worth about $500 Canadian.
4. Juma rented a car in Australia for $280 Australian. About how
much will this cost in C$? Explain your estimate.
e.g., AU$1 =· C$0.9288 That’s 10¢ less, so I can take 10% of the Australian amount and subtract it: AU$280 – (10% of $280) is about $280 – $30 or about C$250.
5. Rosa is ordering goods from South Africa, for 1250 rand.
How can you estimate the price in Canadian dollars?
e.g., C$1 is about 7 rand, so I can round the amount in rand and divide by 7: 1400 rand  7 is about C$200
Copyright © 2011 by Nelson Education Ltd.
06C06.indd 177
Chapter 6
Working with Money
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Chapter
1. Calculate each unit price.
a) 3 shrubs for $145.50 c) 200 g for $69.98
$69.98  200 =· $0.35/g
$145.50  3
= $48.50/shrub
b) $10.99 for 4 kg
d) 250 L for $362.50
$10.99  4 = $2.75/kg
$362.50  250 = $1.45/L
2. Jelani is choosing between a 300 g package of cheddar
cheese for $4.57 and a 450 g package for $7.65. Which
package has a lower unit price?
e.g., $4.57  300 g = $0.015/g
$7.65  450 g = $0.017/g
The 300 g package has a lower unit price.
3. Dalton is trying to attract more members to his gym.
Memberships usually cost $649/year with a sign-up fee of
$75. He offers two promotions:
• Fitness promotion: no sign-up fee
• Strength promotion: 15% off total fee
Which promotion is less expensive for a 12-month
membership?
e.g., Fitness: $649
Strength: regular price: $649 +$75 = $724
discount: 15% of $724 = $108.60
cost: $724 – $108.60 = $615.40
The Strength promotion is less expensive.
4. Ramona is a travel agent. She has found a 30% off deal for
her client. The regular price for the trip is $850 per person.
How much does the trip cost with the 30% discount?
e.g., $850 x 0.70 = $595
The trip costs $595.
178
06C06.indd 178
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:43:04 PM
5. Karlee provides maid service to residential homes. She would
like to increase her prices by 15%. She currently charges $18/h.
a) What would Karlee’s new hourly rate be?
e.g., $18/h x 1.15 = $20.70/h
Her new rate would be $20.70/h.
b) Karlee is currently working 40 h a week. How much more
would she be making after the increase?
e.g., $20.70 – $18 = $2.70
$2.70 x 40 = $108
She would be making $108 more per week.
6. David wants to take cooking classes. One cooking school
offers 12 classes for $552.50. If he signs up before the end of
the week, he will get a 20% discount.
a) How much will the classes cost with the 20% discount?
e.g., $552.50 x 0.80 = $442.00
The classes will cost $442.00.
b) How much would David be paying per class before the
discount and after the discount?
e.g., $552.50  12 classes = $46.04/class
$442  12 classes = $36.83/class
David would be paying $46.04 before the discount, and
$36.83 after the discount.
7. In 2010, many people travelled to Vancouver to participate in
the Olympics. If an athlete from Japan brought 100 000 yen,
how much is this in Canadian dollars if ¥1 =∙ C$0.011?
e.g., JP¥100 000 x 0.011 C$/JP¥ =· C$1100
Apprenticeship & Workplace GR 10
8. Jonathan travelled to Mexico
for business. He paid
0-17-650271-8
C$899 for the trip and spent an additional 1400 pesos
C06-F20-AW10WB
FN
while in Mexico.
CO
CrowleArt Group
a) Estimate the value ofTechnical
MX$1400 in Canadian
dollars.
Deborah Crowle
3rd pass
Pass
C$140
e.g., MX$1400  10 =
b) Calculate the cost
Approved
Approved
of Not
Jonathan’s
trip in Canadian dollars.
MX$1400 x C$0.081/MX$ =· C$113.40
C$899 +C$113.40 = C$1012.40
Copyright © 2011 by Nelson Education Ltd.
06C06.indd 179
Chapter 6 Working with Money
179
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chapter
1. Isoke manages a shoe store. A shipment of 24 pairs costs
$743.52. Before she sells the shoes, she calculates the price
per pair and adds 112% to the unit price. How much profit
does Isoke make per pair?
e.g., Cost: $743.52  24 = $30.98
Selling price: $30.98 x 2.12 = $65.68
Profit: $65.68 – $30.98 = $34.70
Isoke makes $34.70 profit per pair of shoes.
2. Trevor has two offers to consider for lift passes for
snowboarding at his favourite hill. The regular price for a lift
pass is $87.
• Jump offer: buy one get another at half off
• Rail offer: 20% off each pass
a) If Trevor wants to buy 10 lift passes, which offer is a better
price?
e.g., Jump (5 x $87) +(5 x $43.50) = $652.50 ←better
Rail: (10 x $87) – 20% x (10 x $87) = $696
b) If Trevor wants to buy 2 lift passes, which offer is a better
price?
e.g., Jump: $87 +$43.50 = $130.50 ←better
Rail: (2 x $87) – 20% x (2 x $87) = $139.20
Hint
You can look
up the current
exchange rate or
use these.
C$1 = US$0.967
C$1 = €0.676
C$1 = JP¥90.198
3. Suppose you had $500 Canadian. Calculate the amount of
money that would be in each currency.
a) US dollars
e.g., C$500 x US$0.967/C$ = US$483.50
b) Euros
e.g., C$500 x €$0.676/C$ = €338
c) Japanese yen
e.g., C$500 x JP¥90.198/C$ = JP¥45 099
180
06C06.indd 180
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:43:05 PM
6
Hint
A percent is a
fraction out of 100.
getting
1. Write each percent as a decimal.
a) 25% =
0.25
d) 7% =
b) 15% =
0.15
e) 1.5% = 0.015
c) 47% =
0.47
f ) 12.5% = 0.125
0.07
2. Calculate.
a) 25% of 500 =
125
d) 35% of 300 =
105
b) 6% of 35.50 =
2.13
e) 2.5% of 50 =
1.25
c) 10% of 1650 =
165
f ) 0.5% of 29 = 0.145
3. Write each decimal as a percent.
a) 0.65 =
65%
d) 0.04 =
b) 0.12 =
12%
e) 0.055 = 5.5%
c) 0.1 =
f ) 0.002 =
10%
4%
0.2%
4. Write each fraction as a percent. Round to the nearest tenth.
2
1 ∙
a)
= 40%
c)
= 33.3%
5
3
b)
5
= 62.5%
8
d)
4 ∙
= 133.33%
3
5. Complete the chart.
156
06C06.indd 156
Fraction
Decimal
Percent
1
4
3
10
4
5
9
8
123
100
59
1000
0.25
25%
0.3
30%
0.8
80%
Apprenticeship and Workplace 10
1.125
1.23
0.059
112.5%
123%
5.9%
Copyright © 2011 by Nelson Education Ltd.
4/20/10 1:42:45 PM
6. Calculate the total cost of each item, including GST.
To determine GST, calculate 5% of the price.
a) MP3 player for $79.99
GST: $79.99 × 0.05 = $ 4.00
Total: $79.99 + $ 4.00 = $ 83.99
b) laptop for $549.99
GST: $549.99 x 0.05 = $27.50
Total: $549.99 +$27.50 = $577.49
Hint
GST stands
for Goods and
Services Tax.
Some provinces
have an additional
provincial sales tax
called PST. Some
provinces combine
the PST and GST
and charge a
harmonized sales
tax, HST.
7. Calculate.
a)
1
4
of 500 =
125
d)
3
5
of 300 =
180
b)
1
3
of 30 =
10
e)
1
5
of 200 =
40
c)
1
10
f)
1
2
of 29 =
of 1650 =
165
14.5
8. Suppose you have a coupon for 10% off a meal.
Calculate the price of each meal.
a) total: $56.98
$56.98 − (10% of $56.98)
= $56.98 − $ 5.70
= $ 51.28
b) total: $19.57
$19.57 − (10% of $19.57)
= $19.57 − $ 1.96
= $ 17.61
9. Sasha likes to tip 15% on the cost of services.
Estimate the tip on each purchase.
a) hair cut: $68
15% of $68 = (10% of $68) + (5% of $68)
e.g., =∙ $ 7
+ $ 3.50
=∙ $ 10.50
b) taxi fare: $23
15% of $23 = (10% of $23) + (5% of $23)
e.g., =∙ $ 2.50 + $ 1.25
=∙ $ 3.75
Copyright © 2011 by Nelson Education Ltd.
06C06.indd 157
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Working with Money
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Mid-chapter
1. Calculate the unit cost for 100 g.
a) cheese at $12.80/kg
$12.80  10 = $1.28/100 g
b) sausage at $2.89 for 375 g
$2.89/375 g x 100 = $0.77/100 g
2. Olivia is buying equipment for her wholesale bakery.
a) She can get two mixers for $3396 or three mixers for
$4794. Which option is the lower unit price?
$3396  2 = $1698
$4794  3 = $1598
3 mixers for $4794 is the lower unit price.
b) What factors other than price might Olivia consider when
buying mixers?
e.g., safety, durability, warranty, how many she needs
3. Koli sells 2 kg of frozen turkey breasts for $32.55 and 300 g of
fresh turkey breasts for $7.89. Which is the lower unit price?
2 kg = 2000 g
$32.55  2000 g = $0.016/g ← lower $7.89  300 g = $0.026/g
4. Calculate each sale price.
a) 35% off $780
c) 5% off $198
$780 – (35% of $780) = $507
$198 – (5% of $198) = $188.10
b)
1
3
off $780
$780 – ( 31 of $780) = $520
d) 12.5% off $36
$36 – (12.5% of $36) = $31.50
5. Peter is a locksmith. After he ran ads in the newspaper, his
company’s sales increased by 4.2% from the previous year.
His sales were $206 890 the previous year. What were his
sales after the ads ran?
CARLTON LOCKS
• Security
• Value
$206 890 x 1.042 = $215 579.38
His company’s sales were $215 579.38 after the ads.
Copyright © 2011 by Nelson Education Ltd.
06C06.indd 167
Chapter 6
Working with Money
555-LOCK
167
4/20/10 1:42:51 PM
Lines and Angles
7
Tina is a carpenter who specializes in wood flooring. When she
lays the flooring, she is careful to keep the pieces straight. When
she creates a design, she likes to vary the angles.
A. What angles do you think are used most often in carpentry?
e.g.,rightangles(90),45angles,straightangles(180);
possibly30anglesand22.5angles
B. What tools can be used to measure angles and lines?
e.g.,forangles:aprotractor,acarpenter’ssquare(for90),
thegaugeonamitresaw,ananglebevelgauge
forparallellines:ameasuringtapeorruler,alevel
forperpendicularlines:acarpenter’ssquare,aplumbline
Copyright © 2011 by Nelson Education Ltd.
07C07.indd 181
Chapter 7
Lines and Angles
181
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7.1
Estimating and Measuring Angles
Try These
You will need
• square paper
• a protractor
i) The 3 angles in ∆ARE form a straight line, which measures
ii) What is the measure of ∠E? 180° –
84
–
29
=
180 .
67
A
84°
R
?
29°
?
E
84°
29°
You can tell the measure of some angles without measuring.
2
1
What is the angle measure of a square corner of paper? 90
2
What angle measure do you get when you fold a square along
its diagonal? 45
3
What angle measure do you get when you fold the square
1
so that the diagonal meets the base? 222
3
AW10
You can C07-F09-AW10.eps
use referents like the angles above to estimate the
REFLECTING
Figure Number
0-17-650271-8
What referents
Company
for angles do
Technical
you use?
Pass
Approved
measures of other angles.
1st Pass
Example
1
Estimate the measure of each angle marked on the sketch of the
roof truss. (The first one is done for you.)
Not Approved
0-AW10.eps
2
1
s
3
1: a bit less than 90°
Estimate: about 70°
184
07C07.indd 184
2: e.g., a lot more than 90°
Estimate: e.g., about 135°
Apprenticeship and Workplace 10
3: e.g., about half of 45°
Estimate: e.g., about 20°
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:09 PM
Solution
A. Draw a dotted line to show how close the angle is to 90°
or 180°.
B. Estimate the angle measure by comparing it with the referent
angle you drew in Part A.
Example 2
What is the measure of the reflex angle at the peak of the roof truss?
Solution 1
A. Extend an arm to form a straight angle.
180°
41°
B. Measure the acute angle in the arc using a protractor and
add it to 180°.
180° + 41 = 221
Solution 2
A. Measure the obtuse angle using a protractor. 139
B. Subtract that measure from the total number of degrees
around a point.
360° – 139 = 221
REFLECTING
Do you prefer
Solution 1 or
Solution 2? Why?
Example 3
The elevation angle of a solar panel on a house should be between
AW10 wants to install solar
25° and 70°. Albert, a building contractor,
0-17-650271-8
panels on a roof at an angle of 55°. Draw
a 55° angle for the roof.
Figure Number
Solution
A. Draw one arm of the angle.
C07-F12b-AW10.eps
Company
Technical
Pass
Hint
The centre mark
of the protractor
should be on
the vertex. The
baseline of the
protractor should
be on one arm.
1st Pass
Approved
Not Approved
B. Use a protractor to locate a point
on the other arm.
Draw this arm.
AW10
C. Mark the arc and label the angle
measure.
0-17-650271-8
Figure Number
C07-F13-AW10.eps
Company
Technical
Pass
55°
1st Pass
Approved
Not Approved
Copyright © 2011 by Nelson Education Ltd.
07C07.indd 185
Chapter 7
Lines and Angles
185
4/20/10 4:30:09 PM
Practice
45°
1. Sketch the smallest angle for each move of 45°
the needle on a
compass. Label the angle measure.
N
NE
NW
W
E
SW
a) from N to W
c) from NW to SE
SE
S
180°
180°
90°
90°
b) from E to SE
d) from S to NW
45°
135°
135°
45°
?
2. Calculate the measure of the equal angles between any two
180°
arms of a wind
turbine.
3603=120
180°
C07-F15-AW10.eps
Hint
When three
letters are used
to name an angle,
the middle letter
identifies the vertex
of the angle.
1st Pass
3. Estimate the measure of ∠ABC in each diagram. Draw dotted
AW10
lines
AW10to show the referent angles you used.
0-17-650271-8
0-17-650271-8
ANumber
a)Figure
Figure Number
Company
Company
Technical
Technical
Pass
Pass
Approved
Approved
135°
B Approved
Not
Not Approved
135°
c)
A
C
C
0-17-650271-8
AW10
A
Figure
Number
0-17-650271-8
Company
Figure Number
C07-F21-AW10.eps
Technical
Company
Pass
Technical
C07-F16A-D-AW10.eps
1st Pass Pass
Approved
Not
Approved
1st Pass
186
Approved
Not Approved
07C07.indd 186
E
C07-F16A-D-AW10.eps
D
Estimate: about135
d)
D
B
AW10
C
1st Pass
1st Pass
Estimate: about80 b)
B
C07-F16A-D-AW10.eps
C07-F16A-D-AW10.eps
A
C
B
F
Estimate: about120 Estimate: about35
1st Pass
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
AW10
0-17-650271-8
Figure Number
Company
C07-F19b-AW10.eps
4/20/10 4:30:11 PM
4. Measure and label the two angles at each vertex.
a)
42°
318°
5. Construct each angle.
a) 7°
d) 133°
133°
7°
b) 24°
C07-F22b-AW10.eps
AW10
ny
e) 272°
272°
0-17-650271-8
cal
Figure Number
1st Pass
C07-F23a-AW10.eps
Company
ed
Technical
proved
24°Pass
1st Pass
Approved
Not Approved
c) 51°
f ) 315°
AW10
0-17-650271-8
Figure Number
271-8
mber
b)
227°
133°
50271-8
Number
Hints
• What should the
angle measures
around each
vertex add up to?
• Extend the arms
so that the angle
is large enough
to measure.
C07-F24-AW10.eps
C07-F27-AW10.eps
Company
Technical
Pass
51°
315°
1st Pass
Approved
1st Pass
Not Approved
ved
6. Sonya is building a square table. She wants to finish the
top with wood veneer strips placed at a 45° angle to each
AW10How can she do this without using a protractor?
edge.
0-17-650271-8
e.g.,Drawalinefromonecornertotheotherone,
Figure Number
C07-F28-AW10.eps
1-8
ber
C07-F25-AW10.eps
Company
diagonally,andplacethefirststripalongthatline.
Technical
1st Pass
Pass
1st Pass
Copyright © 2011 by Nelson Education Ltd.
Approved
Chapter 7
Lines and Angles
187
Not Approved
ed
07C07.indd 187
AW10
4/20/10 4:30:12 PM
7.2
Describing Angles
Try These
You will need
• a protractor
adjacent angles
angles that share
a common vertex
and a common
arm
supplementary
angles
two angles whose
sum is 180°
∠2and∠3
ii) Which angles form a straight angle? e.g.,∠3and∠4
iii) Which angles share a common side? e.g.,∠1and∠2
i) Which angles form a right angle?
Angles are often described in
pairs. In this sketch of a
construction crane, ∠ABC and
∠CBD are adjacent angles.
1
2
3
2
4
1
D
C
B
Name another pair of
adjacent angles.
e.g.,∠CBDand∠DBE
E
F
A
Name two adjacent angles that are supplementary.
e.g.,∠BEDand∠DEF
AW10
3
0-17-650271-8
Name two adjacent
angles thatC07-F31-AW10.eps
are not supplementary angles.
Figure Number
e.g.,∠CDBand∠
BDE
Company
Technical
complementary
angles
two angles whose
sum is 90°
Pass
1st Pass
4
Connect C to A Approved
and E to A to form a right angle.
5
Name two adjacent angles that are complementary.
∠CABand∠EAB
Not Approved
AW10
Example 0-17-650271-8
Figure Number
C07-F32-AW10.eps
56°
Calculate the
measures of ∠1 and ∠2.
Company
REFLECTING
How can you check
your calculations
using a protractor?
1
Technical
Solution
Approved
A. What is the measure of ∠2?
Pass
Not Approved
2
46°
1st Pass
90 
56
=
34
B. What is the measure of ∠1? 180–(56+46+34)=44
188
07C07.indd 188
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:14 PM
Practice
1. Label the missing angle measures in each diagram.
a)
113°
54°
x°
b)
c)
e)
f)
65° x°
x° 50°
65°
17°
x°
73°
Figure Number
Company
AW10
2. On each
diagram in Question 1, draw an adjacent angle
0-17-650271-8
thatFigure
is not
complementary
or supplementary. Estimate the
Number
C07-F37b-AW10.eps
C07-F34b-AW10.eps
measure
of
each
angle
you
drew. (Answerswillvary.)
Company
Technical
Technical
Pass
1st Pass
3. BradPass
wants to attach
trim at the top of a wall. The ladder,
Approved
the ground, and the wall form a right triangle.
1st Pass
Approved
Not
Approved
AW10
0-17-650271-8
Figure Number
Company
Technical
Pass
Not Approved
How can you calculate the measure of the angle formed
between the top of the ladder and the wall?
C07-F35b-AW10.eps
AW10
e.g.,Thesumoftheanglesinatriangleis180.
0-17-650271-8
1st Pass
Approved
W10
17-650271-8
gure Number
Figure Number
C07-F38b-AW10.eps
180–90–73
=17
Company
?
ladder
wall
73°
4. EachTechnical
angle around1st
the
centre of the window measures 18°.
Pass
Pass
Not Approved
ass
22° x°
68°
55°
90° x°
y° 35°
0-17-650271-8
chnical
x°67°
36°
AW10
ompany
d)
Approved
a) What
is the sum of all the 18˚ angles in the window?
Not Approved= 180
18x10
AW10
C07-F36b-AW10.eps
b) How
many of these angles would it take to make 90˚?
0-17-650271-8
Figure Number
C07-F39b-AW10.eps
5anglesof18haveasumof90.18x5
=90
1st Pass
pproved
Company
An obtuse angle
is greater than 90°
but less than 180°.
Technical
Pass
ot Approved
1st Pass
Approved
Not by
Approved
Copyright © 2011
Nelson Education Ltd.
07C07.indd 189
Hint
Chapter 7
Lines and Angles
189
4/20/10 4:30:15 PM
7.3
Bisecting Angles
Try These
You will need
• tracing paper
• a protractor
• a compass
bisector
the line that
divides an angle
or line into two
equal parts
i) half of 45° is
ii) double 51° is
22.5
In baseball, the pitcher’s mound is located
on the bisector of the angle at home plate,
∠THF. How can you bisect ∠THS to locate
the shortstop position?
102
S
SS
P
T
1
using tracing paper:
Tracetheangle.Foldinhalf.
2
using
a protractor: Measuretheangle(45),
F
H
1
222)Drawthearmofthisangle.
thendivideby2.(
Example
Use a compass and straightedge to bisect ∠STF.
Solution
REFLECTING
Which method of
bisecting an angle
do you prefer?
Why?
A. Draw an arc on ∠STF.
Label X and Y.
S
AW10
S
C. With centre Y and the same
radius, draw another arc.
Label Z.
S
S
Y
0-17-650271-8
S
Y
Y
Figure Number
C07-F42b-AW10.eps
Y
Company
T
T
T
TechnicalX
X
PassX
T
F
ApprovedX
F
F
1st Pass
F
B. With centreNotX,Approved
draw an arc.
Y
Y
T
190
07C07.indd 190
T
T
T
S
S
Y
S
T
T
T
T
S
X
Apprenticeship and Workplace 10
F
F
F
F
Z
Z
Y
X
X
Y
Y
X
S
X
X
F
Z
Z
F
F
F
D. Use a straightedge to join
T to Z.
Y
X
X
Y
Y
S
S
Y
T
T
T
T
S
S
Y
S
S
Z
Z
Y
X
X
X
X
F
Z
Z
F
F
F
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:17 PM
AW10
0-17-650271-8
Practice
1. Pearl bisected obtuse ∠CAB.
What are the measures of the angles?
∠CAB 98 ∠CAZ 49 ∠ZAB
C
49
2. Shelly and Eric want to share a piece of pie. Draw
an acute angle to represent the piece of pie. Then
construct the bisector to create two equal pieces.
3. Matt looked at his watch and said, “The bisector of the
reflex angle between the hour and minute hands would
be located just before the 2.”
a) Do you agree with Matt? AW10
Yes
Check by bisecting the angle.
0-17-650271-8
Z
A
11 12
10
1
a) 2
9 b)
3
8
Number
b) Where is the bisector of theFigure
obtuse
angle C07-F44-AW10.eps
Company
between the hour and second
hands? Draw it.
Technical
Pass
B
4
7
6
5
1st Pass
4. Taylor says, “Bisecting an acute angle always results in two
Not Approved
equal angles that are acute.” Does
bisecting an obtuse angle
always result in two equal angles that are obtuse? Explain
your thinking.
e.g., No; bisecting an obtuse angle like 100 results in two
Approved
50 angles, which are acute.
5. The struts on this kite are perpendicular bisectors.
Where are bisected angles used in the kite?
The struts show a 180 angle bisected into two 90 angles.
Each 90 angle is bisected into two 45 angles. Each 45
1
AW10
2
angle is bisected into two
22 
angles.
0-17-650271-8
Figure Number
C07-F46-AW10.eps
Company
Technical
Copyright © 2011 by Nelson Education Ltd.
Pass
1st PassChapter 7 Lines and Angles
191
Approved
Not Approved
07C07.indd 191
4/20/10 4:30:17 PM
7.4
Replicating Angles
Try These
You will need
• a protractor
• a compass
• a straightedge
i)
180º
× 100 =
360º
50
ii)
% of circle
Ryan is making a cabinet with
shelves of this shape. To copy
acute ∠B, he uses the following
method.
• Place a compass on vertex B
and draw an arc on ∠ABC.
Label the points of intersection
X and Y.
270º
× 100 =
360º
75
% of circle
A
D
X
B
Y
C
• To start the copy, draw side • Use the compass to measure
BC. Then draw an arc on the
XY on the original angle. Then
copy with the same radius
draw an arc with that radius
you used on the original.
from point Y on the copy.
Label Y on the copy.
Label X on the copy. Draw a
B line from B
Y through X.
C
REFLECTING
Measure the original
angle and the
copied angle. How
do they compare?
X
B
Y
1
C
B
Y
C
AW10
Use0-17-650271-8
a compass and a
Figure
Number to copy
C07-F48-AW10WB
straightedge
X
Company
obtuse ∠D in the trapezoid.
A
D
Technical
Pass
REFLECTING
Which method of
copying an angle do
you prefer? Why?
2
B
2nd Pass
HowApproved
can you copy the angle
Y
using
a protractor? C
Not only
Approved
Measuretheoriginalangleanddraw
C
thenewanglewiththesamemeasure.
AW10
192
0-17-650271-8
Apprenticeship
and Workplace 10
Figure Number
C07-F49a-b-AW10WB
Copyright © 2011 by Nelson Education Ltd.
Company
Technical
07C07.indd 192
Pass
Approved
2nd Pass
4/20/10 4:30:19 PM
Example
Anna is using graphing software to make a pie
chart of her budget. The chart represents the
amount of money that goes for lodging,
expressed as a percent of the total circle.
Copy this angle and determine what percent
of her budget goes for lodging.
lodging
Solution
A. Copy the angle for lodging, using a compass
and a straightedge.
B. Is the measure of the copied angle equal to
the measure of the original angle?
Yes; both angles measure 125.
C. What percent of the circle is represented by
lodging?
125°
360° × 100 =∙
35 %
AW10
Practice
0-17-650271-8
Figure Number
C07-F51a-AW10.eps
Company
1. Emily traced this plan for Technical
stairs from a book. Make a copy of
Pass
1st Pass
the two marked angles under the stairs on
a piece of paper.
Approved
Not Approved
AW10
0-17-650271-8
Figure Number
C07-F51b-AW10.eps
Company
Technical
Pass
1st Pass
Approved
Not Approved
Copyright © 2011 by Nelson Education Ltd.
07C07.indd 193
Chapter 7 Lines and Angles
193
4/20/10 4:30:19 PM
2. In art, the primary colours (red, yellow, and blue) are
combined to make other colours. Stefan saw this colour
wheel on the Internet; it shows 12 equal sectors.
yellow- yellow
green
orangegreen
yellow
bluegreen
orange
blue
redorange
blueviolet
red
violet
violetred
a) Calculate the measure of each acute angle around the
centre of the colour wheel.
360  12 = 30
b) Use the circle diagram
at the right to make a
copy of the 12 equal
sectors.
c) The “warm colours”
extend from yellow to
red. How many degrees
of the circle is that?
5 sectors x 30 = 150
d) What percent of the
colour wheel is covered
by the warm colours?
(Round to one decimal place.)
C07-F53-AW10.eps
1st Pass
5
12
x 100 =· 41.7%
3. Kathryn wants to construct
a star logo for her sports
team. Make a copy of each
angle inside the star.
AW10
a) the0-17-650271-8
acute angle
Figure Number
C07-F54b-AW10.eps
Company
Technical
Pass
1st Pass
Approved
Not Approved
b) the reflex angle
194
0-17-650271-8
Figure Number
Company
07C07.indd 194
Copyright © 2011 by Nelson Education Ltd.
Apprenticeship and Workplace 10
AW10
Technical
AW10
0-17-650271-8
C07-F55a-AW10.eps
Figure Number
Company
C07-F55-AW10.eps
4/20/10 4:30:20 PM
7.5
Classifying Lines and Angles
Try These
>
>
E
G
> C
ABandDC;BCandAD
F
>
>
G
EHandFG
Many flags show parallel lines, A
which are always the same
distance apart, and
>>
perpendicular lines, which are
at right angles. This is the flag
of the Franco-Yukonnais
community—the French
Canadian residents of Yukon. B
(The colours are blue, white, and yellow.)
1
H
D
>
F B
D
>>
> C
>>
B
A
>>
>>
Name the parallel sides in each quadrilateral.
H
A > D
i)
ii)
>
E
>>
>>
>>
>
You will need
• a ruler
• a protractor
• a right triangle
(optional)
C
Which lines inside the flag are parallel? Mark them using
matching arrowheads.
AW10
Hints
AW10
2
•
Use
the
symbol

0-17-650271-8
C07-F59a-b-AW10WB
Figure Number
as a short wayFigure
to Number
Company
write that a lineCompany
is
Technical
parallel to another
Technical
Pass
2nd Pass
3
line.
Pass
Approved
• Use the symbol
⊥
Approved
Not Approved
as a short way to
write that a lineNot
is Approved
4
perpendicular to
another line.
0-17-650271-8
Label the corners of the rectangular flag ABCD. Then name
two pairs
of parallel sides.
ABDCandADBC
C07-F59a-b-AW10WB
Name
two pairs of perpendicular sides.
2nd Pass
e.g.,AB⊥BCandAD⊥DC
Complete the following statement: In a rectangle, the
opposite sides are
, and the adjacent sides are
parallel
AW10
perpendicular .
0-17-650271-8
REFLECTING
Do perpendicular
lines have to be
horizontal and
vertical? Use
examples to
explain.
196
07C07.indd 196
5
Figure Number
C07-F60b-AW10.eps
Draw aCompany
flag that does not
includeTechnical
parallel or
Pass
perpendicular lines in 1st
itsPass
Approved
interior design.
Not Approved
Forexample:
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:23 PM
Many angles are formed by two lines and a transversal.
Below, lines P1 and P2 are intersected by T, a transversal.
1
P1
P2
T
2
3
4
5
6
7
6
8
Name all eight pairs of adjacent supplementary angles.
∠1and∠2,∠2and∠4,∠4and∠3,
∠3and∠1,∠5and∠6,∠6and∠8,
corresponding
angles
two angles formed
by two lines and
a transversal and
located on the
same side of the
transversal
∠8and∠7,∠7and∠5
Pairs of angles can be described in other ways.
For example:
• corresponding angles: ∠1 and ∠5, ∠2 and ∠6
(These pairs are above or below lines P1 and P2.)
AW10
0-17-650271-8
Figure Number
Company
Technical
Pass
opposite angles
non-adjacent
angles that are
formed by two
intersecting lines
• opposite angles: ∠1 and ∠4, ∠2 and ∠3
(These are around an intersection point.)
• alternate interior angles: ∠3 and ∠6
C07-F62-AW10.eps
(These
pairs are inside lines P1 and P2.)
• alternate exterior angles: ∠1 and ∠8
(These
1st Pass pairs are outside lines P1 and P2.)
Approved
Not Approved
Example
What other pairs of corresponding angles, opposite angles, and
alternate angles are in the diagram above?
Solution
A. corresponding angles:
∠3and∠7,∠4and∠8
B. opposite angles:
∠5and∠8,∠6and∠7
C. alternate interior angles:
∠4and∠5
D. alternate exterior angles:
∠2and∠7
Copyright © 2011 by Nelson Education Ltd.
07C07.indd 197
transversal
a line that
intersects two
or more lines
Chapter 7
Lines and Angles
alternate angles
two angles formed
by two lines and
a transversal
and located on
opposite sides of
the transversal
Hint
Look on the
opposite sides of the
transversal, inside
lines P1 and P2.
197
4/20/10 4:30:23 PM
-AW10WB
Practice
qr
t s
mn
p o
w x
z y
i j
l k
1. Four lines intersect to form a quadrilateral.
a) Name a pair of opposite angles that are obtuse.
e.g.,∠oand∠m
b) Name two pairs of corresponding angles.
e.g.,∠m,∠iand∠p,∠l
c) Name two pairs of alternate interior angles.
∠o,∠iand∠p,∠j
d) Name two pairs of alternate exterior angles.
∠m,∠kand∠n,∠l
Hint
Use a ruler and a
protractor to check.
AW10
2. In the diagram for Question 1, are any lines parallel or
perpendicular? How do you know?
e.g.,Therearenoparallellinesbecausethedistancesbetween
thelinesarenotthesame.Therearenoperpendicularlines
0-17-650271-8
Figure Number
C07-F63-AW10.eps
becausetherearenorightangles.
Company
Technical
Pass
1st Pass
Approved
Not Approved
2
1
3
3. Four stunt pilots passed in the air and the jet trails formed two
parallel lines and two transversals.
a) Describe the angles shown on the diagram.
∠1 and ∠2: alternateinteriorangles
∠1 and ∠3: correspondingangles
b) How many pairs of opposite angles are there? 10pairs
4. Christina is wallpapering a room.
She uses a plumb line to mark the
line where the first strip of wallpaper
will be placed. This ensures that the
wallpaper will be vertical even if the
wall is crooked. Describe the parallel
and perpendicular lines.
e.g.,Theplumblineshouldbe
nail
wall
ceiling
plumb line
(string with
weight)
floor
perpendiculartothefloorand
ceilingandparalleltotheendof
thewall.Allthewallpaperedges
shouldbeparalleltotheplumbline.
198
07C07.indd 198
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:24 PM
5. Bruno is building a shed. How can he be sure that the ceiling
and the floor are parallel? (Give at least two different ways.)
e.g.,1.Measurethedistancebetweenfloorandceilingin
Hint
If two lines are
perpendicular to
a third line, then
the two lines are
parallel.
differentplacesandadjustuntilit’salwaysthesame.
2.Measuretheanglesbetweenthefloorandthewalland
theceilingandthewall,andadjustuntiltheyareboth90º.
3.Useacarpenter’slevelandadjustthefloorandceiling
untiltheyarelevel.
6. Name all the pairs of parallel lines and perpendicular lines
in the fridge magnet shown at right.
J
A
AYJS
AY⊥YS
TEA M
JS⊥YS
eur's
Seign d
Lan
nd R
Mill
ow
perpendiculartotheriver.
Y
Seco
7. The seigneurial system was a way of
distributing plots of land in New France from
1627 to 1857. Land was surveyed close to a
river because it was the main transportation
route at that time. How does this system use
parallel and perpendicular lines?
e.g.,Thelotsareparalleltoeachotherand
First
Row
8. Floor joists like this are built in a new house to
ensure that the floor surface is strong.
S
ch
Chur
River
2
1
AW10
0-17-650271-8
a) What type of angles are ∠1 and
∠2?
Figure Number
alternateinteriorangles
Company
C07-F67-A
W10.eps
b) If the horizontal beams in the Technical
joists are parallel,
Pass
2nd Pass
what do you know about these
angles?
Approved
Theyareequal.
Not Approved
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Ltd. Number
Chapter 7
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Lines and Angles
199
Company
Technical
Pass
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7.6
Parallel Lines and Transversals
Try These
You will need
• a protractor
• a compass
• tracing paper
i) Name a pair of opposite angles. e.g.,∠1and∠3
ii) Name a pair of adjacent supplementary angles.
2
1
e.g.,∠1and∠2
3
4
This map of northern Alberta shows that Highway 56 and
Highway 854 are parallel. Highway 13 intersects both of them.
1
4
2
3
854
Ohaton
13
Range Road 183
56
Bawlf
5
6
8
7
13
854
AW10
F
F
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1
Figure
C07-F70-AW10.eps
Name pairs
ofNumber
corresponding
angles labelled on the diagram.
Company
∠1and∠5,∠4and∠8,∠2and∠6,∠3and∠7
Technical
F
Hint
Two corresponding
angles form an F
shape: F, , , or .
Pass
2
Z
Hint
3
Two alternate AW10
0-17-650271-8
interior angles form
Z
a Z shape: Z, ,Figure
, Number
Company
or .
1st Pass
CompareApproved
the measures of the corresponding angles in each
Approved
pair. WhatNotdo
you notice?
Themeasuresofcorrespondinganglesareequal.
Name the pairs of alternate angles labelled on the diagram.
alternate interior angles: ∠3and∠5,∠4and∠6
C07-F71-AW10.eps
Z
alternate exterior angles: ∠2and∠8,∠1and∠7
Technical
Pass
4
Approved
Not Approved
200
07C07.indd 200
1st Pass
Compare
the measures of the alternate angles in each pair.
What do you notice?
Themeasuresofalternateanglesareequal.
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:26 PM
5
Measure ∠4 and ∠5, the interior angles on the same side
of the transversal. What do you notice?
non-adjacentsupplementaryangles;theirsumis180º
6
Measure the exterior angles ∠1 and ∠8 on the same side
of the transversal. What do you notice?
non-adjacentsupplementaryangles;theirsumis180º
Hint
Two interior angles
on the same side
of a transversal
form a C pattern:
, , , or .
Example 1
How can you determine if Range Road 183 is parallel to Hwy 854?
Solution
A. Are the measures of the corresponding angles equal?
e.g.,Yes,∠7andtheacuteanglebothmeasure63º.
B. The corresponding angles are equal ,so the roads must be
.
parallel
C. What is the relationship between corresponding angles and
parallel lines? If a pair of corresponding angles are equal ,
then the lines are
. OR If the lines are
parallel
, then the corresponding angles are equal .
parallel
D. What is the relationship between alternate angles and parallel
lines? If a pair of alternate angles are equal , then the lines
are
. OR If the lines are
, then
parallel
parallel
the alternate angles are equal .
REFLECTING
What other pairs
of angles could
you measure with
a protractor to
determine if the
roads are parallel?
Hint
Use the words
equal, parallel, or
supplementary
to complete the
sentences in
Parts B to E.
E. What is the relationship between interior angles and parallel
lines? If a pair of interior angles are supplementary , then the
lines are
. OR If the lines are
,
parallel
parallel
then the alternate angles are supplementary .
Example 2
At the intersection of Hwy 854 and Hwy 13, there are two pairs
of opposite angles. What can you say about the measures of
opposite angles?
Solution
What are the measures of opposite angles?
∠7and∠5measure63º;∠6and∠8measure117º.
Oppositeanglesareequal.
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Practice
2
>
3
>
7
8
5
4
1. a) S
tate the alternate angles that are equal.
∠1 and ∠2 and ∠8 and ∠7;
∠3 and ∠4 and ∠6 and ∠5
b) S
tate the corresponding angles that are equal.
∠2 and ∠7 and ∠8 and ∠1;
1
6
∠4 and ∠6 and ∠5 and ∠3
2. In each diagram, is AB parallel to CD?
Explain how you know.
a) E
A
c)
C
C
A
47°
F
47°
53°
53
E
127°
127
B
D
D
F
parallel; corresponding parallel; interior angles
angles are equal
B
add to 180º
b) .eps
d)
E
B
A
114°
112°
D
C
F
parallel; e.g., exterior
interior angles are not angles add to 180º
Figure Number
C07-F73-AW10.eps Figure Number
Company
Pass
1st Pass
Approved
Approved
Not Approved
Not Approved
1st Pass
Apprenticeship and Workplace 10
Copyright © 2011 by Nelson Education Ltd.
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Figure
Number
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Technical
Technical
202
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equal
0-17-650271-8
Pass
D
not parallel; alternate 0-17-650271-8
B
113°
F
Company
67°
A
C
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E
C07-F74-AW10.eps
Figure Number
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3. The pyramid of the Louvre Museum (in Paris,
France) was constructed using parallel lines.
How can you determine the size of the marked
angle in the top window by measuring another
angle?
e.g.,Theedgeofthepyramidisatransversal
thatintersectsparallellines.Youcanmeasure
theangleatthebottombecauseitequalsthe
sizeoftheangleatthetop.Theyarecorrespondingangles.
4. The flag of Nepal is unusual because it is not rectangular.
a) Trace and extend the two parallel lines and a transversal
on the flag.
b) Mark a pair of alternate interior angles with dots.
What is the relationship between these angles?
Theyareequalbecausethelinesareparallel.
c) Mark a pair of corresponding angles with arcs.
What is the relationship between these angles?
Theyareequalbecausethelinesareparallel.
d) Mark a pair of perpendicular lines with a little square.
How do you know they are perpendicular?
Measuretheanglebetweenthetwolineswitha
protractor.Ifitequals90º,thelinesareperpendicular.
5. This diagram shows a transversal crossing two lines.
138° 42°
42°
138°
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Figure Number
C07-F79b-AW10.eps
Company
Technical
Pass
1st Pass
a) What angle measures do you know
without measuring?
Approved
Not Approved
oppositeangleis42°;supplementaryanglesare138°
b) Can you conclude that the lines are parallel? Explain.
No.e.g.,youhavetomeasuretodetermineifthelines
arethesamedistanceapartorifinterioranglesare
supplementary.
AW10
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7.7
Calculating Angles
Try These
a
A transversal passes through a rectangle.
i) Name two corresponding angles.
b
c
∠aand∠cor∠band∠d
ii) Name two alternate exterior angles. ∠aand∠d
d
Edie cut some strips of flooring using two horizontal parallel cuts
and one on a 51° angle.
51°
t
1
d1
2
3
>
4
5
d2
6
7
8
>
AW10
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Figure Number
C07-F81-AW10.eps
51°
Company
Technical
REFLECTING
1
What other ways
can you see to
reach the same
answers?
Pass
1st Pass
What is theApproved
measure of each angle? Explain your thinking.
The first one is done for you.
Not Approved
∠1and∠5are51º.Theseanglesandthe51ºangleatthe
toparecorrespondinganglesformedbyatransversaland
parallellines.
∠4is51º,sinceitisopposite∠1.
∠8is51º,sinceitisopposite∠5.
∠2is129ºbecause∠1and∠2aresupplementary.
AW10
∠6isalso129º,sinceitisacorrespondinganglewith∠2.
0-17-650271-8
∠3is129ºbecauseitisopposite∠2.
Figure Number
C07-F82-AW10.eps
∠7isalso129º,sinceitisacorrespondinganglewith∠3.
Company
Technical
Pass
204
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1st Pass
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Not Approved
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4/20/10 4:30:30 PM
Example
60°
This design in a rectangular floor shows many parallel
and perpendicular lines. Determine the measures of
the angles. Explain your thinking.
Solution
A. What is the measure of the eight acute angles across the top
of the diagram? How do you know?
These angles all equal 60º because the wood strips are parallel
and these are corresponding angles.
B. What is the measure of the eight acute angles across the
bottom? How do you know?
These angles all equal 60º. They are alternate interior angles
between parallel sides of the floor.
C. What is the measure of the seven obtuse angles across the
bottom? How do you know?
These angles measure 120º. 120º is supplementary to the
acute angles, which measure 60º. They are interior angles.
AW10
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Figure Number
Practice
C07-F84-AW10.eps
Company
Technical
a) Mark the parallel sides
of the parallelogram.
45°
1st Pass
AW10
135°
45°
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Figure Number
>>
45°
f
135°
135°
45°
135°
>
45°d
C07-F85-AW10.eps
45°
135°
Company
AW10
Technical
0-17-650271-8
Pass
Figure Number
45° Approved
Company
45°Approved
o =Not
Technical
>>
Pass
1. Marty folded a rectangular
piece of paper to formApproved
a
Not
Approved
parallelogram. He labelled
the vertices f, o, l, d and
measured one of the angles,
∠o = 45º.
1st Pass
C07-F85-AW10.eps
135°
l 45°
>
1st Pass
b) Determine the measures of the other
angles in the
Approved
parallelogram. Explain your thinking.
Not Approved
∠f = 135º and ∠l = 135º and ∠d = 45º. e.g., Angles f
Pass
and o and angles l and d are pairs of interior angles between parallel lines, which have a sum of 180º.
c) On the diagram, label the measures of the angles outside
the parallelogram.
AW10
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Education Ltd.
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Company
Technical
07C07.indd 205
Pass
2nd Pass
4/20/10 4:30:30 PM
2. Light refraction can be represented by
two parallel lines and a transversal.
light
glass
in
A
a) If ∠A measures 32°, determine the
measure of ∠B. Explain your thinking.
∠B measures 32º because it’s the C
B
out
alternate exterior angle with ∠A.
b) Determine the measure of ∠C. Explain your thinking.
∠C is 148º because ∠B and ∠C are supplementary.
3. What is the measure of the two
angles in the stair diagram?
Explain your thinking.
The obtuse angle is 132.5º because 227.5°
?
360º – 227.5º = 132.5º. The acute ?
angle is 47.5º because horizontal lines are parallel so these interior angles are supplementary.
4. In this diagram of a roof truss, GX is the bisector of ∠YXZ.
Calculate the measure of each angle below. Explain your
AW10
thinking.
0-17-650271-8
Y
Approved
Not Approved N
>>
70°
1st Pass
AW10
>>
G
0-17-650271-8
E
>
Pass
A
>
Technical
>>>
Company
X
C07-F87-AW10.eps
>>>
Figure Number
L
Z
Figure Number
C07-F88-AW10.eps
a) ∠XGE 70°; alternate
interior angle
with ∠AXG
Company
b) ∠XYG 20°; sumTechnical
of angles in a triangle = 180°
Pass means 2 equal
1st Pass
c) ∠GXE 70°; bisector
angles
Approved
d) ∠XGA 70°; alternate interior angle with ∠GXE
Not Approved
e) ∠YGA 20°; complementary angle with ∠XGA
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Figure Number
C07-F
89-AW10.eps
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and
Workplace 10
Company
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Technical
Pass
1st Pass
Approved
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7.8
Solving a Clock Puzzle
Dan has an old wind-up alarm clock. At
9:00 p.m., he sets the alarm so that the
alarm pointer bisects the reflex angle
formed by the hour and minute hands.
As he looks at the clock, he wonders
how many times the hands form a
90° angle in a day.
A. What strategies can you use to figure
out how many right angles are formed
in 12 h?
e.g.,Youcanuseamodeltofigure
outthatthehourandminutehands
11
12
1
2
10
9
3
6
8
formarightangletwotimesevery
4
7
hour,e.g.,at9:00and9:38,then
6
5
at10:05and10:37.Thenyoucan
usethepatternofarightangle
beingformedaboutevery33minutes.
Therewon’tbetwotimesduringeachofthehoursbecause
there’sonlyonetimeforthe2o’clocksand8o’clocks(around
AW10
2:28and8:28).Soin12hoursthereare2(10)+1+1,or22
0-17-650271-8
Figure Number
rightangles.
C07-F90-AW10.eps
Company
Technical
B. DeterminePass
the number of1sttimes
a right angle is formed in 24 h.
Pass
Approved
Therewillbedouble22,or44,rightanglesformedinaday.
Not Approved
C. At what time did Dan’s alarm clock go off the next morning?
Explain how you know.
e.g.,Thealarmgoesoffat4:30a.m.Theangleat9:00is
90º,sothereflexangleis270º.Halfof270ºis135º.Iused
acircularprotractortofigureoutthatthebisectorgoes
halfwaybetweenthe4and5.
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4/20/10 4:30:31 PM
Chapter
You will need
• a compass
• a straightedge
1. Write three angle measures that are useful as referents when
you estimate angles.
e.g., 45º, 90º, and 180º
Use the circle diagram to help you answer Questions 2 and 3.
2. Visualize a round pizza. What is the measure of each angle if
the pizza is cut into each number of equal pieces?
60º 90º
a) 6
c) 4
b) 12
d) 9
30º 40º
3. Aidan cut a round pizza into eight equal pieces. Then he
bisected one piece. What is the measure of each angle in the
two smallest pieces?
360°  8 = 45º
1
half of 45º = 22 2 º
4. Calculate the measure of each angle.
a) the complement of an angle whose measure is 23°
90º – 23º = 67°
b) the supplement of an angle whose measure is 79°
180º – 79º = 101º
c) the third angle in a triangle whose other angles
measure 35˚ and 66˚
91-AW10.eps
180º – (35º +66º) = 79º
ss
d) the reflex angle around a right angle
360º – 90º = 270º
5. Sketch an angle for each type. Bisect the obtuse angle.
a) obtuse angle
e.g.
208
07C07.indd 208
Apprenticeship and Workplace 10
b) reflex angle
e.g.
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:32 PM
6. A parking lot shows five parallel lines with a transversal. If one
angle measures 90°, what can you say about the measures
of the other angles?
All the other angles equal 90º because corresponding angles
are equal, and each supplementary angle is equal to 90º.
7. Karla is building a fence. She attached the top board to the
first two posts. How can she be sure that the two posts are
parallel to each other?
e.g., Measure the angle formed by one post and the top. Measure the angle formed by the other post and the top. The two interior angles should be supplementary.
8. Brook says that the two lines in this optical illusion are not
parallel. Do you agree or disagree? Explain your thinking.
e.g., Disagree. If you measure with a AW10
ruler, the distance 0-17-650271-8
between the lines at either end is theFigure
same.
Number
C07-F93-AW10.eps
Company
Technical
Pass
1st Pass
Approved
9. Determine the measure of each angle.Not Approved
Explain your thinking.
= 102º; e.g., ∠p and ∠78º are
a) p
p
78°
supplementary
58°
r
u
>>
= 58º; e.g., ∠q and ∠58º are opposite
b) q
angles
c) r =
t
44º; e.g., ∠78º and ∠r +∠q (58º)
v
q
>>
67°
s
are interior angles that are supplementary
since the vertical lines are parallel
d) s =
67º; e.g., ∠s and ∠67º are corresponding angles
e) t =
+∠q (58º) are the sum of
55º; e.g., ∠t +∠s (67º)
AW10
angles in a triangle
f) u =
0-17-650271-8
Figure Number
C07-F94-AW10.eps
Company
113º; e.g., ∠u and ∠67º
are supplementary
Technical
g) v = 125º; e.g., ∠v and ∠t Pass
(55º) are supplementary
1st Pass
Approved
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209
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Chapter
1. Are the angles complementary, supplementary, or neither?
You will need
• a protractor
• a compass
a) 34˚ and 56˚ complementary
c) 99° and 81° supplementary
b) 23˚ and 163˚
d) 74° and 16°complementary
neither
2. a) Estimate the measure of the obtuse
angle shown.
e.g.,greaterthan90º;about95º
48.5° 48.5°
b) Bisect the obtuse angle.
c) Label the measure of each acute angle.
Hint
You can make a
sketch for each
part to help you
answer Question 3.
3. Visualize two lines that are intersected by a transversal. Tell if
any of the lines are parallel, perpendicular, or neither for each
condition given.
a) The corresponding angles are equal.
parallellines
b) The interior angles on the same side of the transversal
are 80˚.
neither
c) The alternate angles are right angles. parallellinesanda
transversalthatisperpendiculartothetwolines
E
N
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ANandLE
Number
C07-F97b-AW10.eps
e.g.,∠AGEand∠NGL
b) Name a pairFigure
of opposite
angles.
G
L
>
>
A
4. a) Name a pairAW10
of parallel lines.
Company
c) Are ∠ANG and
∠LEG equal? Explain your thinking.
Technical
Pass
1st Pass
Yes,theyarealternateinterioranglesbetweenparallellines.
Approved
d) What is the Not
measure
of ∠NAG? Explain your thinking.
Approved
90º.Whenthelinesareparallel,interioranglesonthesame
sideofthetransversalaresupplementary.180º–90º=90º
5. Draw an angle of 20º
using a protractor.
20°
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07C07.indd 210
Apprenticeship and Workplace 10
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4/20/10 4:30:33 PM
7
You will need
• a ruler
• a protractor
Getting
1. Name each of these in ∆ABC. Forexample:
a) a point
B
PorB
b) a line segment
ACorPC
P
c) an angle
∠Aor∠CBA
d) a vertex
AorB
C
A
2. Double the measure of each angle.
a) 14° 28
c) 73.3° 146.6
b) 121° 242
d) 164.8° 329.6
3. Determine the measure of each angle.
a)
1
2
of 172° =
86
b)
1
2
of 81° = 40.5
4. Calculate the measure of each angle.
a) 360° ÷ 2 = 180
c) 360° ÷ 6 =
b) 360° ÷ 60 =
6
60
d) 360° ÷ 12 =
30
5. Determine the measure of each unknown angle.
a) 37° + 53 = 90°
b) 96° + 84 = 180°
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6. Match each typeFigure
of angle
its description.
Number with C07-F02-AW10.eps
Company
right angle
Technical
Pass
straight angle
Approved
an angle less than 90°
1st Pass
a 90° angle
Not Approved
acute angle
obtuse angle
reflex angle
182
07C07.indd 182
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an angle greater than 90° but less
than 180°
a 180° angle
an angle greater than 180° but less
than 360°
Copyright © 2011 by Nelson Education Ltd.
4/20/10 4:30:06 PM
Use the circular protractor diagram to answer Questions 7 to 9.
7. Determine the number of degrees in each.
a) 1 whole circle
360
1
2
of a circle
180
c)
1
4
of a circle
90
110
100 90 80 70
60
50
20
60°
10
25°
20
22
0
340
33
03
00
02
21
0 350
8. Draw a 25° angle on the circular protractor.
Mark the arc and label it 25°.
30
190 180 170 16
01
50
1
40
40
b)
0
13
0
12
31
0
0
30
80 270 260 25
90 2
02
02
40
23
9. On the circular protractor, draw the hour and
minute hands of a clock to show 10:00 p.m.
Mark the arc and label the measure of the acute angle.
>
>
10. What three angle measures are
shown in the chair diagram?
180, 90,and 270
AW10
11. Sketch each pair of line segments.
0-17-650271-8
Figure Number
C07-F04b-AW10.eps
a) a pair of line segments
b) a pair
of line
Company
that are parallel but
segments that are
Technical
are not vertical or
perpendicular
but are
Pass
1st Pass
horizontal
not vertical or horizontal
Approved
perpendicular
at right angles
(90°)
Not Approved
>
>
parallel
always the same
distance apart
12. a) Measure this acute angle using a protractor.
18
AW10
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Technical
Pass
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b) Determine the measure of the reflex angle. 342
Approved
Not Approved
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© 2011 by Nelson
Education Ltd.
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Company
Lines and Angles
183
Company
Technical
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183
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1st Pass
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Mid-Chapter
You will need
• a protractor
• a compass
• a straightedge
1. Name two of each, using letters. For example:
∠DAE, ∠AEC
a) acute angles
b) obtuse angles
∠ABC, ∠BCD
c) straight angles
∠AOD, ∠COE
B
C
125°
A
d) complementary angles ∠FEA and ∠AEC
125°
O
D
25°
e) supplementary angles ∠COD and ∠DOE
2. Use the diagram from Question 1.
a) Estimate the size of ∠FAB. e.g., about 120
65°
F
25°
E
b) Mark an arc for each angle you named in
Question 1 a), b), and d). Then measure
and label each angle measure.
3. The grey areas represent the blind spots
for a driver.
a) Estimate the size of ∠L and ∠R.
∠L is about 70
∠R is about
60
L
AW10
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b) On the diagram, bisect Figure
the Number
larger
Company
blind-spot angle.
C07-F56b-AW10.eps
Technical
c) Make a copy of the smaller
Pass blindspot angle, using a compass
Approved and
a straightedge.
Not Approved
1st Pass
R
4. An equilateral triangle has sides of equal length and
angles of equal measure. What is the measure of each
angle? How do you know?
60º; The sum of the angles in a triangle is 180º.
180º  3 = 60º
AW10
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Copyright © 2011 by Nelson Education Ltd.
Figure Number
Chapter 7 Lines and Angles
C07-F58b-AW10.eps
195
Company
Technical
07C07.indd 195
Pass
1st Pass
4/20/10 4:30:21 PM