Angle Relationships5-1

Learn to classify angles and find their measures.

Angle Relationships5-1

Vocabularyangle adjacent angles

right angle supplementary angles

acute angle complementary angles

obtuse angle

straight angle

vertical angles

congruent angles

Angle Relationships5-1

An angle () is formed by two rays, or sides, with a common endpoint called the vertex.

*You can name an angle several ways: 1) by its vertex

2)by its vertex and a point on each ray 3) by a number.

*When three points are used, the middle point must be the vertex.

Angle Relationships5-1

Angle Relationships5-1

Additional Example 1: Classifying Angles

A. two acute angles

B. two obtuse angles

SQP, RQT

TQP, RQS

Use the diagram to name each figure.

mTQP = 43°; mRQS = 47°

mSQP= 133°; mRQT = 137°

Angle Relationships5-1

Additional Example 1: Classifying Angles

C. a pair of complementary angles

B. two pairs of supplementary angles

TQP, TQR

TQP, RQS

Use the diagram to name each figure.

mTQP + mRQS = 43° + 47° = 90

mTQP + mTQR = 43° + 137° = 180

SQP, SQR mSQP + mSQR = 133° + 47° = 180

Angle Relationships5-1Check It Out: Example 1

A. two acute angles

B. two obtuse angles

AEC, BED

AEB, CED

Use the diagram to name each figure.

mAEB = 15°; mCED = 75°

mAEC= 105°; mBED = 165°

Angle Relationships5-1Check It Out: Example 1

C. a pair of complementary angles

D. a pair of supplementary angles

CED, AEC

AEB, CED mAEB + mCED= 15° + 75° = 90

mCED + mAEC = 75° + 105° = 180

Use the diagram to name each figure.

Angle Relationships5-1

Additional Example 2A: Finding Angle Measures

Use the diagram to find each angle measure.

If m1 = 37°, find m2.

1 and 2 are supplementary.

Substitute 37 for m1.

m1 + m2 = 180°

37° + m2= 180°

m2 = 143°

–37° –37° Subtract 37 from both sides.

Angle Relationships5-1

Additional Example 2B: Finding Angle Measures

Use the diagram to find each angle measure.

Find m3, if m<2= 143°.

2 and 3 are supplementary.

Substitute 143 for m2.

m2 + m3 = 180°

143° + m3 = 180°

m3 = 37°

–143° –143° Subtract 143 from both sides.

Angle Relationships5-1

Check It Out: Example 2

Use the diagram to find each angle measure.

If m1 = 42°, find m2.

1 and 2 are supplementary.

Substitute 42 for m1.

m1 + m2 = 180°

42° + m2= 180°

m2 = 138°

–42° –42° Subtract 42 from both sides.

Angle Relationships5-1

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 angles have 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.

Angle Relationships5-1

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.

Vertical angles are congruent.ABF CBD

mABF = mCBD

mCBD = 26

Congruent angles have the same measure.Substitute 26 for mCBD.

Angle Relationships5-1

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.

The angles are complementary.

Substitute 26 for mCBD.

mCBD + mDEB = 90°

26 + mDEB = 90°

mDEB = 64°

–26° –26° Subtract 26 from both sides.

Angle Relationships5-1

Check It Out: Example 3

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.

Vertical angles are congruent.ABF CBD

mABF = mCBD

mCBD = 19

Congruent angles have the same measure.Substitute 19 for mCBD.

19

Angle Relationships5-1

Check It Out: 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.

The angles are complementary.

Substitute 19 for mCBD.

mCBD + mDEB = 90°

19 + mDEB = 90°

mDEB = 71°

–19° –19° Subtract 19 from both sides.

19

Angle Relationships5-1

Lesson QuizUse the diagram to name each figure or find each angle measure.

1. a right angle

3. pair of complementary angles

4. If m1 = 47°, then find m3.

5. Find m4.

2. two acute angles

Possible answer: CGD

Possible answer: 3, 4

Possible answer: 1, 2

47°

43°