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 Additional Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. 71° + m1 = 90° –71° m1 = 19° Since the angles are complementary, the sum of the angle measures is 90 °. 1 71° A. The angles are complementary. Subtract 71° from both sides.

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

6. Holt CA Course 1 9-4 Finding Angle Measures m3 = 82° Congruent angles have the same measure. 382° C. The angles are vertical angles. Additional Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. Since the angles are vertical angles, the angles are congruent.

7. 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. Additional Example 2: 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.

8. 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. Additional Example 2 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.

9. Holt CA Course 1 9-4 Finding Angle Measures b = 27°Vertical angles are congruent. Additional Example 2 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.

10. Holt CA Course 1 9-4 Finding Angle Measures Check It Out! Example 1 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 °.

11. Holt CA Course 1 9-4 Finding Angle Measures –22° 22 ° + z = 90° The sum of the measures is 90°. z = 68° Subtract 22° from both sides. Check It Out! Example 2 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.

12. Holt CA Course 1 9-4 Finding Angle Measures –165° 165 ° + x = 180° The sum of the measures is 180°. x = 15° Subtract 165° from both sides. Check It Out! Example 2 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

13. Holt CA Course 1 9-4 Finding Angle Measures y = 22°Vertical angles are congruent. Check It Out! Example 2 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

14. 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°

15. 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°

16. Holt CA Course 1 9-4 Finding Angle Measures 31 ° + m4 + 31° = 180° –62° 62 ° + m4 = 180° The sum of the measures is 180°. D. BEA  CED; mAED = 180 ° m4 = 118° Subtract 62° from both sides. 4 31° E C B DA Additional Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. Since BEA and CED are congruent, mCED = 31 °. mBEA + mBEC + mCED = 180 °. Add. Substitute.

17. Holt CA Course 1 9-4 Finding Angle Measures Check It Out! Example 1 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 °.

18. Holt CA Course 1 9-4 Finding Angle Measures Check It Out! Example 1 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.

19. 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° Subtract 50° from both sides. Check It Out! Example 1 Find each unknown angle measure. Since WZV and XZY are congruent, mXZY = 25 °. mWZV + mWZX + mXZY = 180 ° Add. Substitute. b 25° Z X W YV