What are we going to do? - Weebly

1

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.


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.


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


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


Skill Development/Guided Practice 1 (continued)

Go to

Concept Dev 2

Determine the property of angles needed.


Substitute the given angle measure(s) into the equation.

Solve the equation.



1

2

3

a

b


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


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


m∠A + m∠B = 90°


m∠A + m∠B = 180°



Measure: _____________________


Measure: _____________________

Adjacent Angles

m∠A + m∠B = m∠C

Vertical Angles

m∠A = m∠B




Solve the equation.



1

2

3

a

b


CFU

1

2a

Skill Development/Guided Practice 2


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






Solve the equation.



1

2

3

a

b



Measure: _____________________


Measure: _____________________m∠x = 75

m∠x = 75

vertical

87 = m∠x

m∠x = 87

87

x

75x

vertical

Adjacent Angles


Vertical Angles

m∠A = m∠B


CFU

1

2a



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


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?





Solve the equation.



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


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°


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


Measure: _____________________


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




Solve the equation.



1

2

3

a

b

Adjacent Angles


Vertical Angles

m∠A = m∠B


m∠A + m∠B = 90°


m∠A + m∠B = 180°





Solve the equation.



1

2

3

a

b

Adjacent Angles


Vertical Angles

m∠A = m∠B


m∠A + m∠B = 90°


m∠A + m∠B = 180°



Measure: _____________________


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


Independent Practice (continued)

63 + 51 + m∠x = 180


51 y

38x

63

z



– 114– 114m∠x = 66

114 + m∠x = 180

38 + m∠y = 66– 38– 38

m∠y = 28

m∠z = 51


Periodic Review 1

Access Common Core




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°.


Periodic Review 2

Access Common Core



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.


Periodic Review 3

Access Common Core


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:

Documents

What are we going to do? - Weebly