1. Angle Relationships 7-1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Angle Relationships 7-1 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

3. Angle Relationships 7-1 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? 1616 1313

4. Angle Relationships 7-1 Learn to classify angles and find their measures.

5. Angle Relationships 7-1 Vocabulary angle adjacent angles right anglesupplementary angles acute anglecomplementary angles obtuse angle straight angle vertical angles congruent angles

6. Angle Relationships 7-1 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.

7. Angle Relationships 7-1

8. Angle Relationships 7-1 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°

9. Angle Relationships 7-1 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

10. Angle Relationships 7-1 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°

11. Angle Relationships 7-1 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.

12. Angle Relationships 7-1 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.

13. Angle Relationships 7-1 Additional Example 2B: Finding Angle Measures Use the diagram to find each angle measure. Find m3 = 37°. 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.

14. Angle Relationships 7-1 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.

15. Angle Relationships 7-1 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.

16. Angle Relationships 7-1 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.

17. Angle Relationships 7-1 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.

18. Angle Relationships 7-1 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

19. Angle Relationships 7-1 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

20. Angle Relationships 7-1 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

21. Angle Relationships 7-1 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°

22. Angle Relationships 7-1 1. If m1 = 42°, then find m3. A. 3° B. 42° C. 48° D. 90° Lesson Quiz for Student Response Systems

23. Angle Relationships 7-1 2. Name a pair of complementary angles. A. CGD B. AGF C. AGB,BGC D. CGD,DGF Lesson Quiz for Student Response Systems

24. Angle Relationships 7-1 3. Find mCGD. A. 3° B. 42° C. 90° D. 180° Lesson Quiz for Student Response Systems