Download Angles and Equations Essential

Math 7
Unit Outline Title: Angles and Equations
Essential Question(s):
How are the different angles created by intersecting lines related?
How do I use the properties of special pairs of angles to solve problems?
How do I write and solve algebraic equations to find unknown variables and angles in a figure?
MCC7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi‐step
problem to write and solve simple equations for an unknown angle in a figure.
Assessment Description/Performance Task:
Constructed response
Informal assessment
Performance task
Selected response
Brief Description:
Instructional Methods
Introduction to Unit: Unpack the standards with the students. Suggestion: Highlight the verbs, circle the
nouns, and discuss the meaning of each word. Prompt students to circle additional words in the
standards that they are unfamiliar with.
Day 1: Learning Target: Today I will learn about angle pairs because intersecting lines form special
relationships that help me solve problems.
Launch: Have students draw/create a pair of intersecting lines (they can use spaghetti noodles,
pipe cleaners, draw them individually, or the teacher can draw them on the white board or using
technology). Students then measure the different angles and as a class or an individual written
assignment, they discuss what they notice about the different angles. This leads into what we call
the different pairs of angles.
Teach: Go through the graphic organizer and answer the questions on Reading Strategies:
Angles.
Vocabulary Activity: Put students in pairs of groups of three. Each pair/group gets a Frayer
model with one of the vocabulary words in the center (adjacent, linear pair, complementary,
supplementary, vertical). They fill in only one box of the Frayer model. After a minute or two,
they pass their Frayer model to another pair/group. They then fill in another box of the new
Frayer model. Repeat this 4 times until all boxes are filled in. Share completed Frayer models
and post outstanding ones in the room.
Summary: Have students fill in the blank: I really understand ______________, but I’m still not
sure about __________________.
Other Suggested resources: Gizmo (Investigating Angle Theorems Activity A) at
www.explorelearning.com , or create a Flip Book.
Assess student understanding by having students complete Mastery Pairs of Angles WS
and/or Name the Relationship WS.
Day 2: Learning Target: Today I will determine angle measures from a diagram.
Use the power point Determining Angle Measures of Intersecting Lines, which begins with a
Do-Now or Warm-Up
Teach: In the power point, students will watch a video from Khan Academy at
http://www.khanacademy.org/math/geometry-1/core-geometry/v/angles-at-the-intersection-oftwo-lines . ***Please Note, if the video doesn’t play, just click the download button at the
bottom right hand corner and it will download and play from there.
After the video, students will go through the examples in the power point, or, you can also work
through examples on the Khan Academy website at
http://www.khanacademy.org/exercise/complementary_and_supplementary_angles . You can
turn on the scratchpad and show work in different colors.
Assess student understanding by selecting a variety of worksheets at
http://www.mathworksheets4kids.com/angles.html
Day 3: Learning Target: Today I will write and solve equations to find missing angle measures.
CCSD Version Date: March 2012
Warm-Up/Do-Now: Students will complete the writing piece on explaining the steps of finding
different angle measures.
Teach: Students go through the Class Notes on writing and solving equations using angle pair
relationships. There are four examples that you will work through as a class. You can do these
using white boards or have students complete on their own note sheet. This was adapted from
www.betterlesson.com (search for Solve Equations with Angles.)
Students then work through the independent practice. Students can work individually or in pairs.
A group of students may be selected to work in a group with the teacher. For co-taught classes,
this is a great opportunity for parallel teaching or station teaching.
Summarize: Exit Ticket/ Ticket Out the Door (if you run out of time, you can use this as a
warm up the next day)
Assess student understanding by the independent practice and Exit Ticket.
Day 4: Learning Target: Today I will write and solve equations to find missing angle measures.
Review notes and practice from the day before
Activity: Scavenger Hunt: Copy the scavenger hunt on colored paper and hang the papers
around the room. Instruct students to number their papers from 1 to 12 and then go with their
partner to one of the colored papers. Each scavenger hunt page is divided into two sections - an
answer at the top and a problem at the bottom. Students will work the problem at the bottom of
the page. When they have an answer, they should look around the room to find the scavenger
hunt page with that answer at the top. They should go to that scavenger hunt page and work
that problem as their second problem. Students will continue in this manner until they have
completed all twelve problems. After students have completed their 12th problem, they should
end at the first scavenger hunt page. If they return to their first scavenger hunt page before they
have completed all twelve problems, they have made an error and need to go back and check
their work.
Assess student understanding by observing and addressing issues that arise during the activity.
If time permits, go ahead and begin the performance task for day 5.
Day 5: Learning Target: Today I will create a city using my knowledge of angle pairs and their
relationships.
Students will complete the City Project in groups of 3 or 4.
CCSD Version Date: March 2012
Name
LESSON
1-4
Date
Class
Reading Strategies
Use a Graphic Organizer
The graphic organizer below outlines the different possibilities for a pair of angles.
adjacent—two angles in the same
plane with a common vertex and
a common side but no common
interior points
complementary—two
angles whose measures
have a sum of 90
linear—adjacent
angles whose
noncommon sides
are opposite rays
vertical—two
nonadjacent
angles formed
by two intersecting lines
Angle pairs
can be
supplementary—two
angles whose measures
have a sum of 180°
Identify each pair of angles as complementary, supplementary, linear,
vertical, or adjacent. Use the graphic organizer above to help you.
Keep in mind that there may be more than one answer for each exercise.
2.
1.
complementary
vertical
3.
4.
supplementary
linear or supplementary
5.
6.
adjacent
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
complementary
34
Holt Geometry
Name
LESSON
1-4
Date
Class
Name
Reteach
LESSON
Pairs of Angles
1-4
continued
Complementary Angles
Supplementary Angles
sum of angle measures is 180�
�
�
�
�
�
�
�
�
m�3 � m�4 � 180�
m�1 � m�2 � 90�
In each pair, �3 and �4 are
supplementary.
In each pair, �1 and �2 are
complementary.
Class
Challenge
Investigating Angle Measurement
For greater accuracy in angle measurement, each degree can be divided into
60 equal parts, called minutes (1� � 60�). Each minute can be further divided
into 60 equal parts, called seconds (1�� 60�).
Angle Pairs
sum of angle measures is 90�
Date
Given a decimal angle measure, you
can convert it to degrees and minutes.
Given an angle measure in degrees and minutes,
you can convert it to a decimal measure.
67.2� � 67� � 0.2�
� 67� � (0.2 � 60)�
� 67� � 12�, or 67�12�
119� 51� � 119� � 51�
51 �
� 119� � ___
60
� �
� 119� � 0.85�, or 119.85�
Find the measure of the complement of each angle using degrees,
minutes, and seconds.
2.
1.
Tell whether each pair of labeled angles is complementary,
supplementary, or neither.
�������
37.76°
11.
10.
52� 14� 24�
����
����
���
Find the measure of the supplement of each angle using degrees, minutes,
and seconds.
���
complementary
5� 12�
neither
4.
3.
152.375°
��������
Find the measure of each of the following angles.
12. complement of �S
34�
13. supplement of �S
124�
14. complement of �R
68�
15. supplement of �R
158�
64� 48�
27� 37� 30�
Use the figure for Exercises 5–8.
���
�
5. Name a pair of supplementary angles.
�
Sample answer: �KLM and �MLN
6. Name a pair of vertical angles whose measures have a
sum that is less than 180�.
���
�
�
�
�
�
�
�
�
�
�
Sample answer: �KLH and �MLN
16. �LMN and �UVW are complementary. Find the measure of each angle if
m�LMN � (3x � 5)� and m�UVW � 2x �.
�
7. If m�HJK � (3x � 2)�, what is the measure of �KJM?
180 � (3x � 2)� or (178 � 3x)�
�
_
m�LMN � 56�; m�UVW � 34�
8. Suppose HQ is drawn on the figure. Name a pair of vertical
angles that is formed.
Sample answer: �HCK and �RCQ
31
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name
LESSON
1-4
Date
Holt Geometry
Class
Problem Solving
LESSON
1-4
Pairs of Angles
Use the drawing of part of the Eiffel Tower for Exercises 1–5.
1. Name a pair of angles that appear to be
complementary.
Y
2. Name a pair of supplementary angles.
Class
Holt Geometry
Reading Strategies
Use a Graphic Organizer
adjacent—two angles in the same
plane with a common vertex and
a common side but no common
interior points
A
M
3. If m�CSW � 45�, what is m�JST ? How do
you know?
W
S
D
J
R
�
complementary—two
angles whose measures
have a sum of 90�
C
K
Z
linear—adjacent
angles whose
noncommon sides
are opposite rays
�
�
�
B
L
Sample answer: �AML and �YML
45�; they are vertical angles.
Date
The graphic organizer below outlines the different possibilities for a pair of angles.
X
Sample answer: �ALB and �BLC
32
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name
T
F
vertical—two
nonadjacent
angles formed
by two intersecting lines
Angle pairs
can be
E
���
4. If m�FKB � 135�, what is m�BKL? How do
you know?
�
�
supplementary—two
angles whose measures
have a sum of 180°
���
45�; the angles are supplementary.
���
���
5. Name three angles whose measures sum to 180�.
Sample answer: �ABM, �MBK, and �KBC
Identify each pair of angles as complementary, supplementary, linear,
vertical, or adjacent. Use the graphic organizer above to help you.
Keep in mind that there may be more than one answer for each exercise.
Choose the best answer.
6. A landscaper uses paving stones for a walkway.
Which are possible angle measures for a� and b�
so that the stones do not have space between them?
A 50�, 100�
C 75�, 105�
B 45�, 45�
D 90�, 80�
��
�
�
H 158�
G 112�
J 180�
complementary
A �R is acute.
vertical
3.
4.
�
����
���
supplementary
8. �R and �S are complementary. If m�R � (7 � 3x)� and m�S � (2x � 13)�,
which is a true statement?
B �R is obtuse.
���
���
7. The angle formed by a tree branch and the part of the trunk above it is 68�.
What is the measure of the angle that is formed by the branch and the part
of the trunk below it?
F 22�
2.
1.
��
linear or supplementary
5.
C �R and �S are right angles.
D m�S � m�R
6.
�
�
���
adjacent
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
33
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
�
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
66
���
complementary
34
Holt Geometry
Holt Geometry
CCSD Version Date: March 2012
Describe in words
Describe in words
Sketch examples
Sketch examples
Sketch examples
Sketch examples
Describe in words
Describe in words
Name
LESSON
1-4
Date
Class
Review for Mastery
Pairs of Angles
Angle Pairs
Adjacent Angles
have the same vertex and
share a common side
Linear Pairs
adjacent angles whose
noncommon sides are
opposite rays
Vertical Angles
nonadjacent angles formed
by two intersecting lines
⬔1 and ⬔2 are adjacent.
⬔3 and ⬔4 are adjacent
and form a linear pair.
⬔5 and ⬔6 are vertical
angles.
Tell whether ⬔7 and ⬔8 in each figure are only adjacent, are adjacent and form a
linear pair, or are not adjacent.
2.
1.
3.
Tell whether the indicated angles are only adjacent, are adjacent and
form a linear pair, or are not adjacent.
4. ⬔5 and ⬔4
5. ⬔1 and ⬔4
6. ⬔2 and ⬔3
Name each of the following.
7. a pair of vertical angles
8. a linear pair
9. an angle adjacent to ⬔4
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30
Holt Geometry
Name
LESSON
1-4
Date
Class
Review for Mastery
Pairs of Angles
continued
Angle Pairs
Complementary Angles
sum of angle measures is 90
Supplementary Angles
sum of angle measures is 180
m⬔3 m⬔4 180
m⬔1 m⬔2 90
In each pair, ⬔1 and ⬔2 are
complementary.
In each pair, ⬔3 and ⬔4 are
supplementary.
Tell whether each pair of labeled angles is complementary,
supplementary, or neither.
11.
10.
Find the measure of each of the following angles.
12. complement of ⬔S
13. supplement of ⬔S
56°
S
14. complement of ⬔R
15. supplement of ⬔R
22°
R
16. ⬔LMN and ⬔UVW are complementary. Find the measure of each angle if
m⬔LMN (3x 5) and m⬔UVW 2x.
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31
Holt Geometry
LESSON
1-4
Practice A
1-4
Complete the statements.
side
, but no common interior points.
Use the figures for Exercises 3 and 4.
90
4. complement of ⬔Y
.
right angle
Supplementary
measure of the angle.
.
132
6. An angle is its own complement. Find the measure of a supplement to this angle.
angles are two angles whose measures
135
have a sum of 180.
6. The kind of angle formed by the noncommon sides of two adjacent and
straight angle
supplementary angles is a
7. ⬔DEF and ⬔FEG are complementary. m⬔DEF (3x 4)°, and m⬔FEG (5x 6)°.
Find the measures of both angles. m⬔DEF
.
Draw your answer in the space provided.
8. Sketch ⬔1 and ⬔2 so that
they form a linear pair.
Find the measures of both angles. m⬔DEF
9. Name a pair of vertical angles.
Possible answers: ⬔1 and ⬔3
In an equilateral triangle, all three sides have equal lengths
and all three angles have equal measures. Find the measure
of the following angles.
9. supplement of ⬔A
120
30
or ⬔2 and ⬔4
10. Name a linear pair of angles.
Possible answers: ⬔1 and ⬔2; ⬔2 and ⬔3; ⬔3 and ⬔4; or ⬔1 and ⬔4
!
11. ⬔ABC and ⬔CBD form a linear pair and have
equal measures. Tell if ⬔ABC is acute, right,
or obtuse.
Draw your answer in the space provided.
11. Sketch ⬔1 and ⬔2 so that
they are vertical angles.
91; m⬔FEG 89
Use the figure for Exercises 9 and 10.
In 2004, several nickels were minted to commemorate the Louisiana
Purchase and Lewis and Clark’s expedition into the American West. One
nickel shows a pipe and a hatchet crossed to symbolize peace between
the American government and Native American tribes.
3AMPLEANSWER
10. complement of ⬔A
29; m⬔FEG 61
8. ⬔DEF and ⬔FEG are supplementary. m⬔DEF (9x 1)°, and m⬔FEG (8x 9)°.
3AMPLEANSWER
7. Sketch ⬔1 and ⬔2 so that
they are adjacent angles.
3AMPLEANSWER
27
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All rights reserved.
Holt Geometry
LESSON
1-4
Pairs of Angles
1. Draw two intersecting lines and label the resulting
angles with the numbers 1, 2, 3, and 4.
2. Label ⬔1 with x . ⬔1 and ⬔2 are supplementary.
Find the measure of ⬔2 and label the diagram.
45°; 45°
28
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Practice C
Draw your answers in the space provided.
right
__›
12. ⬔KLM and ⬔MLN are complementary. LM
bisects ⬔KLN. Find the measures of ⬔KLM
and ⬔MLN.
1-4
:
(110 8x)
5. An angle measures 12 degrees less than three times its supplement. Find the
4. The kind of angle formed by the noncommon sides of two adjacent and
complementary angles is a
9
X 137.9
3. supplement of ⬔Z
3. Complementary angles are two angles whose measures have a sum of
LESSON
180
___›
QR
2. Name the ray that ⬔PQR and ⬔SQR share.
2. A linear pair is a pair of adjacent angles whose noncommon sides
are opposite rays.
5.
Pairs of Angles
1. ⬔PQR and ⬔SQR form a linear pair. Find the sum of their measures.
vertex
1. Adjacent angles are two angles in the same plane with a common
and a common
Practice B
LESSON
Pairs of Angles
Holt Geometry
Review for Mastery
Pairs of Angles
Angle Pairs
3AMPLEANSWER
X X X Adjacent Angles
have the same vertex and
share a common side
Linear Pairs
adjacent angles whose
noncommon sides are
opposite rays
Vertical Angles
nonadjacent angles formed
by two intersecting lines
3. ⬔3 is also supplementary to ⬔2. Find the measure of ⬔3 and label the diagram.
4. From your work in Exercises 1–3, make a conclusion about the measures
of the vertical angles.
The measures of the vertical angles are equal.
⬔1 and ⬔2 are adjacent.
5. ⬔X is complementary to ⬔Y, and ⬔Z is also complementary to ⬔Y.
Explain why ⬔X and ⬔Z are congruent.
⬔3 and ⬔4 are adjacent
and form a linear pair.
⬔5 and ⬔6 are vertical
angles.
Tell whether ⬔7 and ⬔8 in each figure are only adjacent, are adjacent and form a
linear pair, or are not adjacent.
If m⬔X m⬔Y 90 and m⬔Z m⬔Y 90, then m⬔X and m⬔Z
2.
1.
are both equal to 90 m⬔Y. So m⬔X m⬔Z. Two angles whose
measures are equal are congruent.
Adjacent angles are defined as two angles in the same plane with a common
vertex and a common side, but no common interior points.
adjacent and form
a linear pair
6. ⬔ADB and ⬔CDB are adjacent angles. If the phrase “but no common interior
points” was not part of the definition, name another pair of angles that would
qualify as adjacent.
3.
only adjacent
not adjacent
Tell whether the indicated angles are only adjacent, are adjacent and
form a linear pair, or are not adjacent.
Possible answer: ⬔ADB and ⬔ADC
only adjacent
4. ⬔5 and ⬔4
Draw your answer in the space provided.
7. Draw a diagram that shows why the
definition of adjacent angles includes
the phrase “in the same plane.”
5. ⬔1 and ⬔4
not adjacent
6. ⬔2 and ⬔3
adjacent and form a linear pair
Use the figure for Exercises 8 –10.
This diagram shows a ray of light reflecting off a mirror.
When light reflects, the incident angle and the reflected
angle are congruent, that is, ⬔1 ⬔2. Find the measure
of ⬔1 in each situation below.
8. ⬔1 ⬔3
9. ⬔3 is a right angle
60
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45
29
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name each of the following.
7. a pair of vertical angles
10. m⬔1 2m⬔3
8. a linear pair
Possible answers:
⬔1 and ⬔6, ⬔2 and ⬔5
Possible answers: ⬔1 and ⬔2;
⬔1 and ⬔5; ⬔5 and ⬔6; ⬔6 and ⬔2
72
9. an angle adjacent to ⬔4
Holt Geometry
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All rights reserved.
65
001_072_Go08an_CRF_c01.indd 30
⬔3
30
Holt Geometry
Holt Geometry
3/23/07 2:36:22 PM
LESSON
1-4
Review for Mastery
Pairs of Angles
LESSON
1-4
continued
For greater accuracy in angle measurement, each degree can be divided into
60 equal parts, called minutes (1 60). Each minute can be further divided
into 60 equal parts, called seconds (1 60 ).
Angle Pairs
Complementary Angles
sum of angle measures is 90
Supplementary Angles
sum of angle measures is 180
Given an angle measure in degrees and minutes,
you can convert it to a decimal measure.
67.2 67 0.2
119 51 119 51
51 119 ___
60
67 (0.2 60)
67 12, or 6712
In each pair, ⬔3 and ⬔4 are
supplementary.
In each pair, ⬔1 and ⬔2 are
complementary.
Given a decimal angle measure, you
can convert it to degrees and minutes.
m⬔3 m⬔4 180
m⬔1 m⬔2 90
Challenge
Investigating Angle Measurement
119 0.85, or 119.85
Find the measure of the complement of each angle using degrees,
minutes, and seconds.
2.
1.
Tell whether each pair of labeled angles is complementary,
supplementary, or neither.
37.76°
11.
10.
52 14 24
5 12
Find the measure of the supplement of each angle using degrees, minutes,
and seconds.
complementary
neither
4.
3.
152.375°
Find the measure of each of the following angles.
12. complement of ⬔S
34
13. supplement of ⬔S
124
27 37 30
Use the figure for Exercises 5–8.
56°
14. complement of ⬔R
68
15. supplement of ⬔R
158
64 48
S
5. Name a pair of supplementary angles.
+
Sample answer: ⬔KLM and ⬔MLN
6. Name a pair of vertical angles whose measures have a
sum that is less than 180 .
22°
R
&
,
*
(
-
#
'
0
.
Sample answer: ⬔KLH and ⬔MLN
16. ⬔LMN and ⬔UVW are complementary. Find the measure of each angle if
m⬔LMN (3x 5) and m⬔UVW 2x .
7. If m⬔HJK (3x 2), what is the measure of ⬔KJM?
1
180 (3x 2) or (178 3x)
2
_
m⬔LMN 56; m⬔UVW 34
8. Suppose HQ is drawn on the figure. Name a pair of vertical
angles that is formed.
Sample answer: ⬔HCK and ⬔RCQ
31
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
LESSON
1-4
001_072_Go08an_CRF_c01.indd 31
Holt Geometry
Problem Solving
LESSON
1-4
Pairs of Angles
4/11/07 3:08:19 PM
Use the drawing of part of the Eiffel Tower for Exercises 1–5.
1. Name a pair of angles that appear to be
complementary.
Holt Geometry
Reading Strategies
Use a Graphic Organizer
The graphic organizer below outlines the different possibilities for a pair of angles.
adjacent—two angles in the same
plane with a common vertex and
a common side but no common
interior points
X
Sample answer: ⬔ALB and ⬔BLC
32
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Y
A
M
2. Name a pair of supplementary angles.
B
L
Sample answer: ⬔AML and ⬔YML
linear—adjacent
angles whose
noncommon sides
are opposite rays
W
3. If m⬔CSW 45, what is m⬔JST ? How do
you know?
complementary—two
angles whose measures
have a sum of 90
C
K
S
Z
45; they are vertical angles.
D
J
T
R
F
vertical—two
nonadjacent
angles formed
by two intersecting lines
Angle pairs
can be
E
4. If m⬔FKB 135, what is m⬔BKL? How do
you know?
supplementary—two
angles whose measures
have a sum of 180°
45; the angles are supplementary.
5. Name three angles whose measures sum to 180.
Sample answer: ⬔ABM, ⬔MBK, and ⬔KBC
Identify each pair of angles as complementary, supplementary, linear,
vertical, or adjacent. Use the graphic organizer above to help you.
Keep in mind that there may be more than one answer for each exercise.
Choose the best answer.
6. A landscaper uses paving stones for a walkway.
Which are possible angle measures for a and b so that the stones do not have space between them?
A 50, 100
C 75, 105
B 45, 45
D 90, 80
A complementary
vertical
3.
4.
J 180
supplementary
8. ⬔R and ⬔S are complementary. If m⬔R (7 3x) and m⬔S (2x 13),
which is a true statement?
A ⬔R is acute.
B ⬔R is obtuse.
7. The angle formed by a tree branch and the part of the trunk above it is 68.
What is the measure of the angle that is formed by the branch and the part
of the trunk below it?
F 22
H 158
G 112
2.
1.
B linear or supplementary
5.
C ⬔R and ⬔S are right angles.
D m⬔S m⬔R
6.
adjacent
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All rights reserved.
33
Copyright © by Holt, Rinehart and Winston.
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Holt Geometry
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66
complementary
34
Holt Geometry
Holt Geometry
Name :
Score :
Teacher :
Date :
Name the relationship: complementary, linear pair, vertical, or adjacent.
/_ j
/_ m
1)
2)
/_ n
/_ a
___________
3)
___________
4)
_
/ e
_
/ d
_
/ r
___________
___________
_
/ q
/_ k
5)
6)
_
/ g
_
/ t
/_ c
___________
___________
/_ f
7)
8)
___________
_
/ b
/_ h
___________
_
/ p
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Name the relationship: complementary, linear pair, vertical, or adjacent.
/_ j
/_ m
1)
2)
/_ n
/_ a
Adjacent
___________
3)
Adjacent
___________
4)
_
/ e
_
/ d
_
/ r
Linear Pair
___________
Vertical
___________
_
/ q
/_ k
5)
6)
_
/ g
_
/ t
/_ c
Linear Pair
___________
Complementary
___________
/_ f
7)
8)
Linear Pair
___________
_
/ b
/_ h
Adjacent
___________
_
/ p
Math-Aids.Com
Warm-Up
On the lines below, explain how you find the measure of
ABC.
C
D
1210
A
B
Remember, a great essay:
- Answers the question completely
E
- Uses vocabulary words
- Contains no statements that are not accurate/true
- Describes the steps taken and why (try using the word because at least once)
Warm-Up
On the lines below, explain how you find the measure of
C
ABC.
D
1210
A
B
Remember, a great essay:
- Answers the question completely
E
- Uses vocabulary words
- Contains no statements that are not accurate/true
- Describes the steps taken and why (try using the word because at least once)
CCSD Version Date: March 2012
Class Notes
Example 1:
C
3x0 510
A
B
D
E
What is the value of x?
What is the measure of angle ABC? Show your work.
Answer:
degrees
--------------------------------------------------------------------------------------------Example 2:
C
A
(6x + 19)0 x0
D
B
E
Part A What is the value of x? Show your work.
Part B What is the measure of angle ABC? Show your work.
Answer:
degrees
What are some math words we should use to explain our answer to Part B?
CCSD Version Date: March 2012
Class Notes
C
Example 3:
(2x-11)0
A
510
F
D
B
E
What is the value of x?
What is the measure of angle ABF? Show your work.
Answer:
degrees
Example 4:
C
780
A
B
(5x –2)0
D
E
Part A What is the value of x? Show your work.
Part B What is the measure of angle DBE? Show your work.
Answer:
degrees
What are some math words we should use to explain our answer to Part B?
CCSD Version Date: March 2012
Independent Practice
1) Write and solve an equation to find the value of x and the measure of each angle labeled.
Work Space:
(2x - 11)
105
X = ____________
2) Find the value of x. Then find the measure of the unknown angle.
Equation: ______________________________
62
(x + 10)
x = ________
Unknown angle = ____________
CCSD Version Date: March 2012
3)
4) D and G are supplementary angles. The measure of
What is the degree measure of D ?
D is 4 times the measure of
5) Solve for x. Then explain how you found the value of x.
(3x + 12)°
72°
CCSD Version Date: March 2012
G.
23
(4x +10)0
500
What is the value of x?
30
C
A
(3x +5)0 (x+15)
B
0
D
What is the measure of angle ABC?
125
(x+5)0
(x - 15)0
What is the value of x?
50
m 1=
(x+4)0
m 2 = (5x + 8)0
What is the measure of angle 1?
17
C
0
A
(3x)
B
(x + 8)0
D
What is the measure of angle CBD?
51
(2x - 11)0
1050
What is the value of x? ______
58
(2x + 10)° 60°
What is the value of x? ______
55
100° (4x − 8)°
What is the value of x?
22
30°
(5x + 10)°
What is the value of x?
10
52°
(3x − 1)°
What is the value of x?
13
155°
(5x)°
What is the value of x?
5
(2x + 24)°
70°
What is the value of x? ______
Name: ____________________________
Date:___________________
CITY PROJECT
You will work in a group. Each group should have the following roles filled by
different students:
City Planner (makes up the names of streets and buildings)
___________________
Architect (builds/draws the streets and buildings)
___________________
Supplier (gathers/delegates supply list for the group) ___________________
Councilman (checks design has all requirements/appearance)
___________________
You and your group are to design your own city and include the following:
1. City name and population at the top of the project
2. Two parallel streets (each street must be named)
3. One street intersecting the two parallel streets (each street must be named)
4. One street that is perpendicular to the two parallel streets with an additional
street creating complementary angles (each street must be named)
The following buildings must be placed as directed:
5. The hospital and the hardware store are supplementary angles
6. Your house and school must be vertical angles
7. Courthouse and bank must be complementary angles
8. The Gas station and a Restaurant form a linear pair
9. Traffic light at two intersections or more (draw 3 circles on top of each other just
like a stop light)
10. The police station and the gas station are vertical angles
11. The fire station is supplementary to the courthouse and the bank
12. Name and label each building
13. Use crayons or colored pencils to draw your city or use 3-dimensional objects.
BE CREATIVE!!!!!
14. Turn in this sheet with your project
CHECKLIST:
ITEM
Streets (named)
Hospital (named)
Police Station (named)
Gas station
(named/location)
Restaurant
CCSD Version Date: March 2012
POINTS POSSIBLE
5
8
8
8
8
POINTS RECIEVED
(named/location)
House (named/location)
School (named/location)
Courthouse
(named/location)
Bank (named/location)
Hardware Store
(named/location)
Fire Station
(named/location)
Traffic lights
(named/location)
General appearance
8
8
8
8
8
8
5
10
A Sample Layout
Fire Station
House
Courthouse
School
Bank
Gas
Station
Restaurant
Police
Station
CCSD Version Date: March 2012
Hardware
Store
Hospital