1. Holt CA Course 1 9-4 Finding Angle Measures Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 9-4 Finding Angle Measures Warm Up Tell whether the given angles are vertical, complementary, or supplementary. 1.  QXT and  QXR 2.  QXR and  TXS 3.  PXQ and  QXR 4.  PXQ and  PXS 5.  TXS and  SXR supplementary vertical complementary supplementary

3. Holt CA Course 1 9-4 Finding Angle Measures MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Also covered: AF1.1, MG2.1 California Standards

4. Holt CA Course 1 9-4 Finding Angle Measures Objective: You will learn how to (YWLHT) use angle relationships to find angle measures.

5. Holt CA Course 1 9-4 Finding Angle Measures Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. Since the angles are complementary, the sum of the angle measures is 90 °. a 71° A. The angles are complementary.

6. Holt CA Course 1 9-4 Finding Angle Measures Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. a 71° + m  a = 90° –71° a m  a = 19° Since the angles are complementary, the sum of the angle measures is 90 °. a 71° A. The angles are complementary. Subtract 71° from both sides.

7. Holt CA Course 1 9-4 Finding Angle Measures a 125° B. The angles are supplementary. Since the angles are supplementary, the sum of the angle measures is 180 °. Example 2: Finding an Unknown Angle Measure Find each unknown angle measure.

8. Holt CA Course 1 9-4 Finding Angle Measures a 125° + m  a = 180° –125° a m  a = 55° Subtract 125° from both sides. a 125° B. The angles are supplementary. Since the angles are supplementary, the sum of the angle measures is 180 °. Example 2: Finding an Unknown Angle Measure Find each unknown angle measure.

9. Holt CA Course 1 9-4 Finding Angle Measures a 82° C. The angles are vertical angles. Example 3: Finding an Unknown Angle Measure Find each unknown angle measure. Since the angles are vertical angles, the angles are congruent.

10. Holt CA Course 1 9-4 Finding Angle Measures a m  a = 82° Congruent angles have the same measure. a 82° C. The angles are vertical angles. Example 3: Finding an Unknown Angle Measure Find each unknown angle measure. Since the angles are vertical angles, the angles are congruent.

11. Holt CA Course 1 9-4 Finding Angle Measures The sum of the measures is 180°. D.  BEA   CED; m  AED = 180° a 31° E C B DA Example 4: Finding an Unknown Angle Measure Find each unknown angle measure.

12. Holt CA Course 1 9-4 Finding Angle Measures a 31° + m  a + 31° = 180° –62° a 62° + m  a = 180° The sum of the measures is 180°. D.  BEA   CED; m  AED = 180° a m  a = 118° a 31° E C B DA Example 4: Finding an Unknown Angle Measure Find each unknown angle measure.

13. Holt CA Course 1 9-4 Finding Angle Measures Check It Out! Example 5 Find each unknown angle measure. 65° + m  d = 90° –65° m  d = 25° Subtract 65° from both sides. d 65° A. The angles are complementary. Since the angles are complementary, the sum of the angle measures is 90 °.

14. Holt CA Course 1 9-4 Finding Angle Measures Check It Out! Example 6 Find each unknown angle measure. 145° + m  s = 180° –145° m  s = 35° Subtract 145° from both sides. s 145° B. The angles are supplementary. Since the angles are supplementary, the sum of the angle measures is 180 °.

15. Holt CA Course 1 9-4 Finding Angle Measures Check It Out! Example 7 Find each unknown angle measure. m  t = 32° Congruent angles have the same measure. t 32° C. The angles are vertical angles. Since the angles are vertical angles, the angles are congruent.

16. Holt CA Course 1 9-4 Finding Angle Measures 25° + b + 25° = 180° –50° –50° 50° + b = 180° The sum of the measures is 180°. D.  WZV   XZY; m  VZY = 180° b = 130° Check It Out! Example 8 Find each unknown angle measure. b 25° Z X W YV

17. Holt CA Course 1 9-4 Finding Angle Measures Home Learning On-Line Tutoring Geo-match-try Geo-fit Geo-Vocab Shape Quiz Geo-Terms

18. Holt CA Course 1 9-4 Finding Angle Measures –27° 27 ° + c = 90° The sum of the measures is 90°. c = 63° Subtract 27° from both sides. Example 9: Application Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. Step 1: The angles labeled c and 27 ° are complementary. To find c, use properties of complementary angles.

19. Holt CA Course 1 9-4 Finding Angle Measures –151° 151 ° + a = 180° The sum of the measures is 180°. a = 29° Subtract 151° from both sides. Example 9 Continued Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. Step 2: The angles labeled a and 151 ° are supplementary. To find a, use properties of supplementary angles.

20. Holt CA Course 1 9-4 Finding Angle Measures b = 27°Vertical angles are congruent. Example 9 Continued Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. Step 3: The angles labeled b and 27 ° are vertical angles. To find b, use properties of vertical angles.

21. Holt CA Course 1 9-4 Finding Angle Measures –22° 22 ° + z = 90° z = 68° Check It Out! Example 10 Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work. x 165° 22° z y Step 1: The angles labeled z and 22 ° are complementary. To find z, use properties of complementary angles.

22. Holt CA Course 1 9-4 Finding Angle Measures –165° 165 ° + x = 180° x = 15° Check It Out! Example 10 Continued Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work. Step 2: The angles labeled x and 165 ° are supplementary. To find x, use properties of supplementary angles. x 165° 22° z y

23. Holt CA Course 1 9-4 Finding Angle Measures y = 22° Check It Out! Example 10 Continued Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work. Step 3: The angles labeled y and 22 ° are vertical angles. To find y, use properties of vertical angles. x 165° 22° z y

24. Holt CA Course 1 9-4 Finding Angle Measures

25. Holt CA Course 1 9-4 Finding Angle Measures

26. Holt CA Course 1 9-4 Finding Angle Measures Home Learning On-Line Tutoring Geo-match-try Geo-fit Geo-Vocab Shape Quiz Geo-Terms

27. Holt CA Course 1 9-4 Finding Angle Measures Lesson Quiz: Part I Find each unknown angle measure. 1. The angles are vertical angles. 2. The angles are supplementary. d = 130° x = 45°

28. Holt CA Course 1 9-4 Finding Angle Measures Lesson Quiz: Part II p = 78° 3.  KNL =  LNM; m  JNM = 180 ° 4. Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. ̃ a = 147°, b = 123°, c = 19°