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Warm Up

Solve.

1. x + 30 = 90

2. 103 + x = 180

3. 32 + x = 180

4. 90 = 61 + x

5. x + 20 = 90

x = 60

x = 77

x = 148

x = 29

x = 70

1

3

1

6

Problem of the Day

Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza?

Sunshine State Standards

MA.8.G.2.2 Classify and determine the measure of angles,…

Vocabulary

angle adjacent angles

right angle supplementary angles

acute angle complementary angles

obtuse angle

straight angle

vertical angles

congruent angles

An angle () is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex.

Additional Example 1: Classifying Angles

Use the diagram to name each figure.

A. two acute angles

TQP, RQS

mTQP = 43°; mRQS = 47°

B. two obtuse angles

SQP, RQT

mSQP= 133°; mRQT = 137°

Additional Example 1: Classifying Angles

Use the diagram to name each figure.

C. a pair of complementary angles

TQP, RQS

mTQP + mRQS = 43° + 47° = 90

B. two pairs of supplementary angles

TQP, TQR

mTQP + mTQR = 43° + 137° = 180

mSQP + mSQR = 133° + 47° = 180

SQP, SQR

Check It Out: Example 1

Use the diagram to name each figure.

A. two acute angles

AEB measures 58° and DEC measures 58°

B. two obtuse angles

AEC measures 148° and DEB measures 122°

Check It Out: Example 1

Use the diagram to name each figure.

C. a pair of complementary angles

AEB measures 58° and DEC measures 32°.58 + 32 = 90°

D. a pair of supplementary angles

AEC measures 148° and DEC measures 32°. 148 + 32 = 180°; AEB measures 58° and DEB measures 122°, 58 + 122 = 180°

Additional Example 2A: Finding Angle Measures

Use the diagram to find each angle measure.

If m1 = 37°, find m2.

m1 + m2 = 180°

1 and 2 are supplementary.

37° + m2= 180°

Substitute 37 for m1.

–37° –37°

Subtract 37 from both sides.

m2 = 143°

Additional Example 2B: Finding Angle Measures

Use the diagram to find each angle measure.

Find m3 = 37°.

m2 + m3 = 180°

2 and 3 are supplementary.

143° + m3 = 180°

Substitute 143 for m2.

–143° –143°

Subtract 143 from both sides.

m3 = 37°

Check It Out: Example 2A

Use the diagram to find each angle measure.

If m3 = 142°, find m4.

m3 + m4 = 180°

142° + m4= 180°

m4 = 38°

–142° –142°

Check It Out: Example 2B

Use the diagram to find each angle measure.

Find m1.

m1 + m4 = 180°

m1 + 38° = 180°

m1 = 142°

–38° –38°

Adjacent angles have a common vertex and a common side, but no common interior points. Angles 1 and 2 in the diagram are adjacent angles.

Congruent angleshave the same measure.

Vertical angles are the nonadjacent angles formed by two intersecting lines. Angles 2 and 4 are vertical angles. Vertical angles are congruent.

Additional Example 3: Application

A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE.

Step 1: Find mCBD.

ABFCBD

Vertical angles are congruent.

Congruent angles have the same measure.

mABF= mCBD

Substitute 26 for mCBD.

mCBD= 26

Additional Example 3 Continued

A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE.

Step 2: Find mDBE.

mCBD + mDEB = 90°

The angles are complementary.

26 + mDEB = 90°

Substitute 26 for mCBD.

–26° –26°

Subtract 26 from both sides.

mDEB = 64°

Check It Out: Example 3

Based on the map, what is the measure of BGC?

AGB is congruent to EGF. mAGB = 42°

mBGC + mAGB = 90°

mBGC + 42° = 90°

mBGC = 48°

Lesson Quiz

Use the diagram to name each figure or find each angle measure.

1. a right angle

Possible answer: CGD

2. two acute angles

Possible answer: 1, 2

3. pair of complementary angles

Possible answer: 3, 4

4. If m1 = 47°, then find m3.

47°

5. Find m4.

43°

Lesson Quiz for Student Response Systems

2. Name a pair of complementary angles.

A. CGD

B. AGF

C.AGB, BGC

D.CGD, DGF

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