SESSION 2 Practice Using Supplementary and Vertical Angles - SharpSchool

LESSON 28 | SESSION 2

Practice Using Supplementary and Vertical Angles

Problem Notes

Assign Practice Using Supplementary and Vertical Angles as extra practice in class or as homework.

1 a.Students should recognize that /DEB and /CEB are supplementary angles, so the sum of their measures is 1 80?. Basic

b.Students should recognize that /AED and /CEBare vertical angles, so their measures are equal. Medium

LESSON 28 | SESSION 2

Name:

Practice Using Supplementary and Vertical Angles

Study the Example showing how to solve problems using supplementary

and vertical angles. Then solve problems 1?5.

Example

k l

k l

? AB and ? CD meet at point E. What is m/AEC?

/AED and /DEB are supplementary angles.

(2x 2 17) 1 (x 1 32) 5 180

3x 1 15 5 180

3x 5 165

x 5 55

/DEB and /AEC are vertical angles.

m/AEC 5 m/DEB

5 (x 1 32)?

5 (55 1 32)?

5 87?

So, m/AEC 5 87?.

D (x 1 32)? B (2x 2 17)? E

A

C

1 Look at the figure in the Example. a. What is m/CEB? Show your work. Possible work: m/DEB 5 m/AEC, and /DEB and /CEB are supplementary, so m/CEB 5 (180 2 87)? 5 93?

SOLUTION m/CEB 5 93?

b. Describe how to find m/CEB another way. Possible answer: Since m/CEB 5 m/AED, you can evaluate 2x 2 17 for x 5 55.

Vocabulary

supplementary angles two angles whose measures sum to 1808.

vertical angles opposite angles formed when two lines intersect. Vertical angles have the same measure.

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LESSON 28 Find Unknown Angle Measures

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Fluency & Skills Practice

Using Supplementary and Vertical Angles

In this activity, students use supplementary and vertical angle relationships to solve for unknown angle measures.

FLUENCY AND SKILLS PRACTICE Name: LESSON 28

Using Supplementary and Vertical Angles

Find the specified angle measures using the information provided.

1 Find m/DBE. C

A

B (x 1 20)?

(5x 2 60)?

E

D

2 Find m/EBD.

E

A

B

(4x 2 2)? (20x 2 10)? D

C

3 Find m/ABC.

A

B

E

(50 2 x)?

(2x 1 40)?

80?

C D

4 Find m/ABC. A

E (9x 2 9)?

(3x 1 9)? B

C

D

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GRADE 7 LESSON 28

Page 1 of 2

617

LESSON 28 Find Unknown Angle Measures

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LESSON 28 | SESSION 2

Additional Practice

2 Students may draw a diagram to help explain their reasoning. They may recall that supplementary angles do not need to be adjacent. Medium

3 After finding the value of x, students could solve the problem by finding m/ACB and subtracting that measure from 180? to find m/DCB. M edium

4 Students should recognize that / DEA and /AEBare supplementary angles because they form a straight angle. Medium

5 Students may draw a diagram of the two angles to understand how the ratio relates to the angle measures. Challenge

LESSON 28 | SESSION 2

2 How can a pair of angles be both vertical and supplementary? They must both be right angles.

3 /ECB and /DCA are straight angles. What is m/DCB? Show your work.

A

E (3x 1 5)? (x 1 11)? C

D

Possible work:

(3x 1 5) 1 (x 1 11) 5 180

B

4x 1 16 5 180

4x 5 164

x 5 41

m/DCB 5 m/ECA 5 [3(41) 1 5]? 5 128?

SOLUTION m/DCB 5 128?

4 ?A?C? and ?D?B? intersect at point E. Find m/BEC and m/DEC. Show your work.

A

(5x 1 36)? E

(3x)?

D

B

Possible work:

3x 1 (5x 1 36) 5 180 m/BEC 5 m/AED

8x 1 36 5 180

5 (3 ? 18)?

C

8x 5 144

5 54?

x 5 18

m/DEC 5 m/AEB

5 [5(18) 1 36]?

5 126?

SOLUTION m/BEC 5 54? and m/DEC 5 126?

5 Two angles are supplementary and their measures have a ratio of 1 : 3. Find the measures of the angles. Show your work.

Possible work:

x represents the measure of the smaller angle.

x 1 3x 5 180

3x 5 3(45)

4x 5 180

5 135

x 5 45

SOLUTION The measures of the angles are 458 and 1358. 618

618 LESSON 28 Find Unknown Angle Measures

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DIFFERENTIATION | ENGLISH LANGUAGE LEARNERS

Use with Session 3 Connect It

Levels 1?3: Reading/Speaking

Prepare for Connect It problem 4 by helping students review the properties of complementary angles and asking them for examples. Allow students to sketch angles, point to figures in the book, or give pairs of angle measurements.

Next, have students draw as you read aloud this paraphrase: A figure has three angles. The angles are /R, /S, and /T. There are two pairs of complementary angles. /R and /S are complementary. /R and /T are also complementary. Ask students to use their drawing to reason about m/S and m/T. Help students craft sentence frames to write their ideas.

Levels 2?4: Reading/Speaking

Help students prepare to respond to Connect It problem 4 by asking them to describe and give examples of complementary angles. If appropriate, ask students to reword responses using precise mathematical language like sum, angle measures, right angle, and congruent.

Next, have students read and make sense of the problem. Ask students to draw the figure described in the problem. Then have them turn to partners, identify the pairs of angles in their drawings, and explain the relationship between the angles. Encourage students to use precise language. After discussing with partners, have students work together to write their explanations.

Levels 3?5: Reading/Speaking

Have students read and make sense of Connect It problem 4 through partner discussion. First, have partners discuss the figure described in the problem. Suggest that students sketch the figure and then explain to partners how they know the pairs of angles are complementary. Reinforce that a clear explanation describes what you noticed or assumed about a problem, what you decided to do as a result, and why.

After partner discussions, have students draft their written responses. If time allows, prompt students to read their responses aloud to partners and ask them to discuss if any details can be revised to make their ideas clearer.

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LESSON 28 Find Unknown Angle Measures

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