1. 9-6 Finding Angle Measures in Polygons Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Warm Up Solve. 1. n + 9 = 37 2. 6 = n - 20 3. 11n = 121 4. 7 = n = 28 n = 26 Course 1 9-6 Finding Angle Measures in Polygons n = 11 n = 49 n7n7

3. Problem of the Day If a triangle has two angles that measure 41° and 117°, what is the measure of the third angle? 22° Course 1 9-6 Finding Angle Measures in Polygons

4. Learn to find angle measures in polygons. Course 1 9-6 Finding Angle Measures in Polygons

5. Course 1 9-6 Finding Angle Measures in Polygons Ray XY crosses at 150°, and ray YZ crosses at 70°. Y X Z Additional Example 1 Use a protractor to find the measure of XYZ. Then classify the angle.

6. Course 1 9-6 Finding Angle Measures in Polygons Y X Z The measure of XYZ is 150°  70°, or 80°. Write this as mXYZ = 80°. Additional Example 1 Continued Use a protractor to find the measure of XYZ. Then classify the angle.

7. Course 1 9-6 Finding Angle Measures in Polygons Y X Z Since 80°< 90°, the angle is acute. Additional Example 1 Continued Use a protractor to find the measure of XYZ. Then classify the angle.

8. Course 1 9-6 Finding Angle Measures in Polygons Y X Z Check Use the other scale on the protractor to find the measure ofXYZ. 110° - 30° = 80°. Additional Example 1 Continued Use a protractor to find the measure of XYZ. Then classify the angle.

9. To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle. Course 1 9-6 Finding Angle Measures in Polygons

10. Additional Example 2: Estimating Angle Measures Estimate the measure of K in parallelogram JKLM. Then use a protractor to check the reasonableness of your answer. Think: The measure of the angle is close to 150°. Course 1 9-6 Finding Angle Measures in Polygons L M J K

11. Additional Example 2 Continued Use the protractor. The measure of the angle is 145°. mK = 145°, so the estimate is reasonable. Use the scale on the protractor that starts with 0°. Caution! Course 1 9-6 Finding Angle Measures in Polygons L M J K

12. Check It Out: Example 2 Estimate the measure of D in parallelogram ABCD. Then use a protractor to check the reasonableness of your answer. Think: The measure of the angle is close to 50°. Course 1 9-6 Finding Angle Measures in Polygons D A B C

13. Check It Out: Example 2 Continued Use the protractor. The measure of the angle is 53°. mD = 53°, so the estimate is reasonable. Course 1 9-6 Finding Angle Measures in Polygons D A B C

14. Additional Example 3: Sports Application The shape of a softball home plate is shown below. Find the measures of C and E. Use a protractor to measure C. CB crosses at 130°, and CD crosses at 40°. Subtract. 130° – 40° = 90° Course 1 9-6 Finding Angle Measures in Polygons A B E C D C = 90°

15. Additional Example 3 Continued The shape of a softball home plate is shown below. Find the measures of C and E. Estimate the mE. It is greater than 90°, so it looks as if the angle measure is 90° + 45°. So, mE is about 135°. Course 1 9-6 Finding Angle Measures in Polygons A B E C D Use a protractor to measure E. E = 135°

16. Check It Out: Example 3 A quadrilateral is shown below. Find the measures of A and C. Use a protractor to measure A. AB crosses at 40°, and AD crosses at 110°. Subtract. 110°  40° = 70° Course 1 9-6 Finding Angle Measures in Polygons A = 70° A B C D

17. Check It Out: Example 3 Continued A quadrilateral is shown below. Find the measures of A and C. Estimate the mC. It is greater than 90°, so it looks as if the angle measure is 90° + 20°. So, mC is about 110°. Course 1 9-6 Finding Angle Measures in Polygons Use a protractor to measure C. C = 110° A B C D

18. Lesson Quiz: Part I Solve each equation. 1. Use the protractor to the measure of ABC. Tell what type of angle it is. 120°, obtuse Insert Lesson Title Here Course 1 9-6 Finding Angle Measures in Polygons

19. Lesson Quiz: Part II Solve each equation. 2.Estimate the measure of B in the parallelogram for Exercise 12 on page 512 of your textbook. Then use a protractor to check the reasonableness of your answer. Insert Lesson Title Here 45° Course 1 9-6 Finding Angle Measures in Polygons