angle relationships 5-1 learn to classify angles and find their measures

Angle Relationships5-1

Learn to classify angles and find their measures.


Vocabularyangle 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: 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.


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°


Additional Example 1: Classifying Angles

C. a pair of complementary angles

B. two pairs of supplementary angles

TQP, TQR

TQP, RQS


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


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



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.


Additional Example 2B: Finding Angle Measures


Find m3, if m<2= 143°.



m2 + m3 = 180°

143° + m3 = 180°

m3 = 37°



Check It Out: Example 2


If m1 = 42°, find m2.



m1 + m2 = 180°

42° + m2= 180°

m2 = 138°



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.


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.


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°



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


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


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°

angle relationships 5-1 learn to classify angles and find their measures

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