Download Measuring and Constructing Angles

Name _________________________________________________________ Date _________
1.5
Measuring and Constructing Angles
For use with Exploration 1.5
Essential Question How can you measure and classify an angle?
1
EXPLORATION: Measuring and Classifying Angles
Go to BigIdeasMath.com for an interactive tool to investigate this exploration.
Work with a partner. Find the degree measure of each of the following angles. Classify
each angle as acute, right, or obtuse.
D
O
B
170 180
60
0 1 20 10 0
15
0 30
14 0
4
80 90 10 0
70 10 0 90 80 110 1
70
2
0
0
1
6 01
60 0 1
2
3
50 0 1
50 0
13
0 10
180 170 1 20 3
60
15 0 4
01 0
40
E
C
A
a. ∠ AOB
b. ∠ AOC
c. ∠ BOC
d. ∠ BOE
e. ∠COE
f. ∠COD
g. ∠ BOD
h. ∠ AOE
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Geometry
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Name_________________________________________________________
1.5
2
Date __________
Measuring and Constructing Angles (continued)
EXPLORATION: Drawing a Regular Polygon
Go to BigIdeasMath.com for an interactive tool to investigate this exploration.
Work with a partner.
a. On a separate sheet of paper or an index card, use a ruler and
protractor to draw the triangular pattern shown at the right.
2 in.
2 in.
120°
b. Cut out the pattern and use it to draw three regular hexagons,
as shown in your book.
c. The sum of the angle measures of a polygon with n sides is equal to 180( n − 2)°.
Do the angle measures of your hexagons agree with this rule? Explain.
d. Partition your hexagons into smaller polygons, as shown in your book. For each
hexagon, find the sum of the angle measures of the smaller polygons. Does each
sum equal the sum of the angle measures of a hexagon? Explain.
Communicate Your Answer
3. How can you measure and classify an angle?
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Geometry
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Name _________________________________________________________ Date _________
1.5
Notetaking with Vocabulary
For use after Lesson 1.5
In your own words, write the meaning of each vocabulary term.
angle
vertex
sides of an angle
interior of an angle
exterior of an angle
measure of an angle
acute angle
right angle
obtuse angle
straight angle
congruent angles
angle bisector
24
Geometry
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1.5
Date __________
Notetaking with Vocabulary (continued)
Postulate 1.3 Protractor Postulate


Consider OB and a point A on one side of OB. The rays of the

form OA can be matched one to one with the real numbers
from 0 to 180.
3
15 0 4
01 0
40
0 10
180 170 1 20
60
A
O
B
170 180
60
0 1 20 10 0
15
0 30
14 0
4
The measure of ∠ AOB , which can be written as m∠ AOB ,
is equal to the absolute value of the difference between the


real numbers matched with OA and OB on a protractor.
80 90 10 0
70 10 0 90 80 110 1
70
2
60 0 110
60 0 1
2
3
50 0 1
50 0
3
1
Notes:
Core Concepts
Types of Angles
A
A
A
acute angle
Measures greater than
0° and less than 90°
A
right angle
obtuse angle
straight angle
Measures 90°
Measures greater than
90° and less than 180°
Measures 180°
Notes:
Postulate 1.4 Angle Addition Postulate
Words If P is the interior of ∠ RST , then the measure of
∠ RST is equal to the sum of the measures of
∠ RSP and ∠ PST .
Symbols If P is in the interior of ∠ RST , then
R
m∠RST
S
m∠RSP
m∠PST
P
m∠ RST = m∠ RSP + m∠ PST .
Notes:
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T
Geometry
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Name _________________________________________________________ Date _________
Notetaking with Vocabulary (continued)
1.5
Extra Practice
In Exercises 1– 3, name three different angles in the diagram.
1.
2.
E
F
G
3.
T
K
Q
H
N
S
L
M
R
In Exercises 4– 9, find the indicated angle measure(s).
4. Find m∠JKL.
5. m∠RSU = 91°.
L
Find m∠RST .
6. ∠UWX is a straight angle.
Find m∠UWV and m∠XWV .
U
M
U
X
W
(x + 20)° x°
85°
31°
S
K
J
69°
V
T
R


7. Find m∠CAD
8. EG bisects ∠ DEF .
9. QR bisects ∠ PQS .
and m∠BAD.
Find m∠DEG and
m∠GEF .
Find m∠PQR and
m∠PQS .
D
Q
C
A
(x + 15)°
(5x + 57)°
S
(−3x + 130)°
D
P
92°
E
G
B
(4x − 10)°
R
F
26
Geometry
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