1. Angle Relationships 5-1 Learn to classify angles and find their measures.

2. Angle Relationships 5-1 Vocabulary angle adjacent angles right anglesupplementary angles acute anglecomplementary angles obtuse angle straight angle vertical angles congruent angles

3. Angle Relationships 5-1 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.

4. Angle Relationships 5-1

5. Angle Relationships 5-1 Additional Example 1: Classifying Angles A. two acute angles B. two obtuse angles SQP, RQT TQP, RQS Use the diagram to name each figure. mTQP = 43°; mRQS = 47° mSQP= 133°; mRQT = 137°

6. Angle Relationships 5-1 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. mTQP + mRQS = 43° + 47° = 90 mTQP + mTQR = 43° + 137° = 180 SQP, SQR mSQP + mSQR = 133° + 47° = 180

7. Angle Relationships 5-1 Check It Out: Example 1 A. two acute angles B. two obtuse angles AEC, BED AEB, CED Use the diagram to name each figure. mAEB = 15°; mCED = 75° mAEC= 105°; mBED = 165°

8. Angle Relationships 5-1 Check It Out: Example 1 C. a pair of complementary angles D. a pair of supplementary angles CED, AEC AEB, CEDmAEB + mCED= 15° + 75° = 90 mCED + mAEC = 75° + 105° = 180 Use the diagram to name each figure.

9. Angle Relationships 5-1 Additional Example 2A: Finding Angle Measures Use the diagram to find each angle measure. If m1 = 37°, find m2. 1 and 2 are supplementary. Substitute 37 for m1. m1 + m2 = 180° 37° + m2= 180° m2 = 143° –37° Subtract 37 from both sides.

10. Angle Relationships 5-1 Additional Example 2B: Finding Angle Measures Use the diagram to find each angle measure. Find m3, if m<2= 143°. 2 and 3 are supplementary. Substitute 143 for m2. m2 + m3 = 180° 143° + m3 = 180° m3 = 37° –143° Subtract 143 from both sides.

11. Angle Relationships 5-1 Check It Out: Example 2 Use the diagram to find each angle measure. If m1 = 42°, find m2. 1 and 2 are supplementary. Substitute 42 for m1. m1 + m2 = 180° 42° + m2= 180° m2 = 138° –42° Subtract 42 from both sides.

12. Angle Relationships 5-1 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.

13. Angle Relationships 5-1 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 mCBD. Vertical angles are congruent. ABF  CBD mABF = mCBD mCBD = 26 Congruent angles have the same measure. Substitute 26 for mCBD.

14. Angle Relationships 5-1 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 mDBE. The angles are complementary. Substitute 26 for mCBD. mCBD + mDEB = 90° 26 + mDEB = 90° mDEB = 64° –26° Subtract 26 from both sides.

15. Angle Relationships 5-1 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 mCBD. Vertical angles are congruent. ABF  CBD mABF = mCBD mCBD = 19 Congruent angles have the same measure. Substitute 19 for mCBD. 19

16. Angle Relationships 5-1 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 mDBE. The angles are complementary. Substitute 19 for mCBD. mCBD + mDEB = 90° 19 + mDEB = 90° mDEB = 71° –19° Subtract 19 from both sides. 19

17. Angle Relationships 5-1 Lesson Quiz Use the diagram to name each figure or find each angle measure. 1. a right angle 3. pair of complementary angles 4. If m1 = 47°, then find m3. 5. Find m4. 2. two acute angles Possible answer: CGD Possible answer: 3, 4 Possible answer: 1, 2 47° 43°