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2Solve for an unknown angle using properties of angles.©2013 All rights reserved.
What are we going to do?
CFU
Students, you already know the measure of a right angle and a straight angle. Now, we will use these angles to help us solve for unknown angles.
Make Connection
We will solve for an unknown angle using properties of angles.
Learning Objective
Activate Prior Knowledge
A right angle is an angle that measures 90.
A straight angle is an angle that measures 180.
Right angle Straight angle
60
+ 30
90
125
+ 55
18030
6055125
1. 2.
Add the angle measures.
3Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Complementary
Angles
Supplementary
Angles
m∠A + m∠B = 90° m∠A + m∠B = 180°
Two angles are
complementary angles
if their sum is 90°.
Two angles are
supplementary angles
if their sum is 180°.
5512530
60
How do you know that figure Ashows complementary angles?
Figure A shows complementary
angles because ____________.
How do you know that figure Bshows supplementary angles?
Figure B shows supplementary
angles because ____________.
CFU 1
1 distinctive feature of
Vocabulary
Concept Development 1
Properties1 of Angles
Complementary
Corner
60+ 30 = 90
60 is the complement of 30.
Supplementary
Straight
Go to Skill Dev 1
7020
A
Complementary
65115
B
Supplementary
70+ 20= 90
115+ 65= 180
125+ 55 = 180
125 is the supplement of 55.
4Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Adjacent
Angles
Vertical
Angles
m∠A + m∠B = m∠C m∠A = m∠B
Two angles are
adjacent angles
if they share a common
ray and endpoint.
Two angles are
vertical angles
if they are formed by two intersecting
lines and are not adjacent.
40
70
Concept Development 2
Properties of Angles
70+ 40= 120
125
125
125= 125
Which of the following figures shows adjacent angles? How do you know?
Explain why the other figure shows vertical angles.
CFU 2
A
B
Go to Skill Dev 2
5Solve for an unknown angle using properties of angles.©2013 All rights reserved.
1. What is the measure of angle x? 2. What is the measure of angle x?
3. What is the complement of a 19 angle? 4. What is the complement of an 85 angle?
Determine2 the property of angles needed.
Solve for the unknown angle measure using the property of angles as follows:
Substitute3 the given angle measure(s) into the equation.
Solve the equation.
Write the solution using the angle measure and degree symbol (m∠x = 45).
Solve for unknown angle measures using properties of angles.
1
2
3
a
b
2 figure out3 replace
Vocabulary
How did I/you determine the property of angles needed?How did I/you substitute the given angle measure(s) into the equation?
CFU
1
2a
Complementary Angles
m∠A + m∠B = 90°
Supplementary Angles
m∠A + m∠B = 180°
x
5035x
Property of Angle: ______________
Measure: _____________________
complementary Property of Angle: ______________
Measure: _____________________
m∠x + 35 = 90
- 35 - 35
m∠x = 55
m∠x = 55
complementary
m∠x + 50 = 90
- 50 - 50
m∠x = 40
m∠x = 40
m∠x + 19 = 90
- 19 - 19
m∠x = 71
m∠x + 85 = 90
- 85 - 85
m∠x = 5
Skill Development/Guided Practice 1
6Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Skill Development/Guided Practice 1 (continued)
Go to
Concept Dev 2
Determine the property of angles needed.
Solve for the unknown angle measure using the property of angles as follows:
Substitute the given angle measure(s) into the equation.
Solve the equation.
Write the solution using the angle measure and degree symbol (m∠x = 45).
Solve for unknown angle measures using properties of angles.
1
2
3
a
b
How did I/you determine the property of angles needed?How did I/you substitute the given angle measure(s) into the equation?
CFU
1
2a
5. What is the measure of ∠1? 6. What is the measure of ∠2?
7. What is the supplement of a 125 angle? 8. What is the supplement of a 30 angle?
1110 68
2
Property of Angle: ______________
Measure: _____________________
supplementary Property of Angle: ______________
Measure: _____________________
m∠1 + 110 = 180
- 110 - 110
m∠1 = 70
m∠1 = 70
supplementary
m∠2 + 68 = 180
- 68 - 68
m∠2 = 112
m∠2 = 112
m∠x + 125 = 180
- 125 - 125
m∠x = 55
m∠x + 30 = 180
- 30 - 30
m∠x = 150
Complementary Angles
m∠A + m∠B = 90°
Supplementary Angles
m∠A + m∠B = 180°
7Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Property of Angle: ______________
Measure: _____________________
Property of Angle: ______________
Measure: _____________________
Adjacent Angles
m∠A + m∠B = m∠C
Vertical Angles
m∠A = m∠B
Determine the property of angles needed.
Solve for the unknown angle measure using the property of angles as follows:
Substitute the given angle measure(s) into the equation.
Solve the equation.
Write the solution using the angle measure and degree symbol (m∠x = 45).
Solve for unknown angle measures using properties of angles.
1
2
3
a
b
How did I/you determine the property of angles needed?How did I/you substitute the given angle measure(s) into the equation?
CFU
1
2a
Skill Development/Guided Practice 2
9. What is the measure of angle x? 10. What is the measure of angle x?
adjacent
- 42 - 42
m∠x = 85
m∠x = 85
m∠x + 42 = 127
adjacent
75 + 35 = m∠x
m∠x = 110
110 = m∠x
7535
x 127
42x
8Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Skill Development/Guided Practice 2 (continued)
Determine the property of angles needed.
Solve for the unknown angle measure using the property of angles as follows:
Substitute the given angle measure(s) into the equation.
Solve the equation.
Write the solution using the angle measure and degree symbol (m∠x = 45).
Solve for unknown angle measures using properties of angles.
1
2
3
a
b
11. What is the measure of angle x? 12. What is the measure of angle x?
Property of Angle: ______________
Measure: _____________________
Property of Angle: ______________
Measure: _____________________m∠x = 75
m∠x = 75
vertical
87 = m∠x
m∠x = 87
87
x
75x
vertical
Adjacent Angles
m∠A + m∠B = m∠C
Vertical Angles
m∠A = m∠B
How did I/you determine the property of angles needed?How did I/you substitute the given angle measure(s) into the equation?
CFU
1
2a
9Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Skill Development/Guided Practice 2 (continued)
23 + m∠x = 61
13. What is the measure of angle x?
61
23
x26 z
14. What is the measure of angle y?
15. What is the measure of angle z?
23
– 23– 23
m∠x = 38
26
38
26 + 38 = m∠y
64 = m∠y
61 + 26 + m∠z = 180
87 + m∠z = 180
– 87– 87
m∠z = 93
How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?
CFU
2
1
3
4
5
y
10Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Solving for unknown angle measures using properties of angles will help
you solve real-world problems.
Solving for an unknown angle using properties of angles
will help you do well on tests.
1
Does anyone else have another reason why it is relevant to solve for unknown angle measures using properties of angles? (Pair-Share) Why is it relevant to solve for unknown angle measures using properties of angles? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?
CFU
2
Relevance
Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180°
Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B
Sample Test Question:
79. What is the supplement of a 40 angle?
A 50
B 130
C 140D 220
40
x
Baker St.
Main St.
First St.
Baker St. intersects Main St. and First
St. forming two complementary angles.
If the orange car turns at a 40 angle,
at what angle will the red car turn?
11Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Determine the property of angles needed.
Solve for the unknown angle measure using the property of angles as follows:
Substitute the given angle measure(s) into the equation.
Solve the equation.
Write the solution using the angle measure and degree symbol (m∠x = 45).
Solve for unknown angle measures using properties of angles.
1
2
3
a
b
What did you learn today about solving for unknown angle measures using properties of angles?(Pair-Share) Use words from the word bank.
Skill Closure
Access Common Core
Summary Closure
Word Bank
angle
complementary
supplementary
adjacent
vertical
unknown
1. What is the measure of angle x?
Property of Angle: __________________
Measure: _____________________
2. What is the measure of ∠1?
Property of Angle: __________________
Measure: _____________________
x48
1108
complementary
m∠x + 48 = 90
- 48 - 48
m∠x = 42
m∠x = 42
supplementary
m∠1 + 108 = 180
- 108 - 108
m∠1 = 72
m∠1 = 72
Which two angles would form complementary angles?
How do you know?
Which two angles would form supplementary angles?
How do you know?
m∠A = 50
m∠B = 30
m∠C = 130
m∠D = 40
Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180°
Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B
m∠A + m∠D = 90°
m∠A + m∠C = 180°
12Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Independent Practice
1. What is the measure of ∠1? 2. What is the measure of angle x?
3. What is the complement of a 51 angle? 4. What is the supplement of a 62 angle?
251
x 136
Property of Angle: ______________
Measure: _____________________
Property of Angle: ______________
Measure: _____________________
complementary
m∠1 + 25 = 90
- 25 - 25
m∠1 = 65
m∠1 = 65
supplementary
m∠x + 136 = 180
- 136 - 136
m∠x = 44
m∠x = 44
m∠x + 51 = 90
- 51 - 51
m∠x = 39
m∠x + 62 = 180
- 62 - 62
m∠x = 118
Determine the property of angles needed.
Solve for the unknown angle measure using the property of angles as follows:
Substitute the given angle measure(s) into the equation.
Solve the equation.
Write the solution using the angle measure and degree symbol (m∠x = 45).
Solve for unknown angle measures using properties of angles.
1
2
3
a
b
Adjacent Angles
m∠A + m∠B = m∠C
Vertical Angles
m∠A = m∠B
Complementary Angles
m∠A + m∠B = 90°
Supplementary Angles
m∠A + m∠B = 180°
13Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Determine the property of angles needed.
Solve for the unknown angle measure using the property of angles as follows:
Substitute the given angle measure(s) into the equation.
Solve the equation.
Write the solution using the angle measure and degree symbol (m∠x = 45).
Solve for unknown angle measures using properties of angles.
1
2
3
a
b
Adjacent Angles
m∠A + m∠B = m∠C
Vertical Angles
m∠A = m∠B
Complementary Angles
m∠A + m∠B = 90°
Supplementary Angles
m∠A + m∠B = 180°
5. What is the measure of angle x? 6. What is the measure of angle x?
Property of Angle: ______________
Measure: _____________________
Property of Angle: ______________
Measure: _____________________
adjacent
85 + 40 = m∠x
m∠x = 125
125 = m∠x
8540
x
Independent Practice (continued)
m∠x = 110
m∠x = 110
110
x
vertical
14Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Independent Practice (continued)
63 + 51 + m∠x = 180
7. What is the measure of angle x?
51 y
38x
63
z
8. What is the measure of angle y?
9. What is the measure of angle z?
– 114– 114m∠x = 66
114 + m∠x = 180
38 + m∠y = 66– 38– 38
m∠y = 28
m∠z = 51
15Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Periodic Review 1
Access Common Core
1. What is the measure of angle x?
2. What is the measure of angle y?
3. What is the measure of angle z?
64°
y
28°
x
77°
z106°
a
28° + m∠x = 64°– 28°– 28°
m∠x = 36°
64° + m∠y = 180°– 64°– 64°
m∠y = 116°
106° + m∠z = 180°– 106°– 106°
m∠z = 74°
Describe how you would find the measure of angle a in the figure above.
(Answers may vary) Angle a is supplementary to the sum of 77° and 64° because it forms a straight angle
with these two angles. To solve for a, subtract the sum of 77° and 64° from 180°.
16Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Periodic Review 2
Access Common Core
1. What is the measure of angle x?
2. What is the measure of angle y?
35° + m∠x = 90°– 35°– 35°
m∠x = 55°
55° + 75° = m∠y116° = m∠y
y35°
x75°
Leonor thinks that the measure of angle x is 16°.
Explain the mistake she made.
x 74°
Matheus thinks that the measure of angle y is 87°.
Explain the mistake he made.
93° y
Leonor confused supplementary angles with complementary
angles. The sum of x and 74° should be 180°, not 90°.
Matheus confused vertical angles with supplementary angles.
Angle y should be 93° because vertical angles are equal in measure.
17Solve for an unknown angle using properties of angles.©2013 All rights reserved.
Periodic Review 3
Access Common Core
1. What is the measure of angle x?
2. What is the measure of angle y?54°
y29°
x
29° + m∠x = 54°– 29°– 29°
m∠x = 25°
54° + m∠y = 180°– 54°– 54°
m∠y = 126°
51° y
38°x
63°
zf
The measure of angle x is equal to the measure of angle y plus 38°.
The measure of angle f is 51°.
The measure of angle x can be found using supplementary angles.
The measure of angle z is 51°.
Choose Yes or No to indicate which of the statements below are true.
O Yes O No
O Yes O No
O Yes O No
O Yes O No
18READY TO TEACHSM EDI ® Lessons©2013 All rights reserved.
EDI Lesson Overview
Standards for Mathematical
Practice (SMPs)
SMP1 Make sense of problems
SMP2 Reason abstractly and
quantitatively
SMP3 Construct arguments and
critique the reasoning of
others
SMP4 Model with math
SMP5 Use appropriate tools
SMP6 Attend to precision
SMP7 Make use of structure
SMP8 Look for regularity in
repeated reasoning
Common Core Shifts
in Mathematics
Shift 1 Focus
Shift 2 Coherence
Shift 3 Fluency
Shift 4 Deep Understanding
Shift 5 Application
Shift 6 Dual Intensity
7th Grade Math
Learning Objective: We will solve for an unknown angle using properties of angles.
Focus Standard: 7.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.
Support Standard: SMP 1, SMP 3, SMP 4, SMP 6
Prerequisite(s):
Manipulative(s):
Special
Instructions:
This is the first time complementary, supplementary, vertical, and
adjacent angles are addressed in the Common Core State Standards.
There is a cognitive strategy to remember the difference between
complementary and supplementary angles. Complementary can be
related to Corner, representing the 90 angle that the two
complementary angles form. Supplementary can be related to
Straight, representing the 180 angle that the two supplementary
angles form.
Vocabulary
Academic: properties, determine, substitute
Content: complementary angles, supplementary angles, vertical angles, adjacent
angles
Support: