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9-6

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

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9-6

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

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

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

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

  5. 9-6 Finding Angle Measures in Polygons Z X Course 1 Additional Example 1: Subtracting to Find Angle Measures Use a protractor to find the measure of XYZ. Then classify the angle. Y • Place the center point of the protractor on the vertex of the angle.

  6. 9-6 Finding Angle Measures in Polygons Z X Course 1 Additional Example 1 Continued Use a protractor to find the measure of XYZ . Then classify the angle. Y • Read the measures where ray XY and ray YZ cross.

  7. 9-6 Finding Angle Measures in Polygons Caution! Ray XY can also be read as crossing at 30°, and ray YZ can be read at crossing at 110°, The angle measure is still the same. Make sure that you read the measures on the same scale. Course 1

  8. 9-6 Finding Angle Measures in Polygons Z X Course 1 Additional Example 1 Continued Use a protractor to find the measure of XYZ . Then classify the angle. Y • Ray XY crosses at 150°, and ray YZ crosses at 70°.

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

  10. 9-6 Finding Angle Measures in Polygons Z X Course 1 Additional Example 1 Continued Use a protractor to find the measure of XYZ . Then classify the angle. Y • Since 80°< 90°, the angle is acute.

  11. 9-6 Finding Angle Measures in Polygons Z X Course 1 Additional Example 1 Continued Use a protractor to find the measure of XYZ . Then classify the angle. Check Use the other scale on the protractor to find the measure ofXYZ. 110° - 30° = 80°. Y

  12. 9-6 Finding Angle Measures in Polygons L N Course 1 Check It Out: Example 1 Use a protractor to find the measure of LMN. Then classify the angle. M • Place the center point of the protractor on the vertex of the angle.

  13. 9-6 Finding Angle Measures in Polygons L N Course 1 Check It Out: Example 1 Continued Use a protractor to find the measure of LMN. Then classify the angle. M • Read the measures where ray LM and ray MN cross.

  14. 9-6 Finding Angle Measures in Polygons L N Course 1 Check It Out: Example 1 Continued Use a protractor to find the measure of LMN. Then classify the angle. M • Ray LM crosses at 50°, and ray MN crosses at 160°.

  15. 9-6 Finding Angle Measures in Polygons L N Course 1 Check It Out: Example 1 Continued Use a protractor to find the measure of LMN. Then classify the angle. M • The measure of LMN is 160°- 50°, or 110°. Write this as m LMN = 110°.

  16. 9-6 Finding Angle Measures in Polygons L N Course 1 Check It Out: Example 1 Continued Use a protractor to find the measure of LMN. Then classify the angle. M • Since 110° > 90°, the angle is obtuse.

  17. 9-6 Finding Angle Measures in Polygons L N Course 1 Check It Out: Example 1 Continued Use a protractor to find the measure of LMN. Then classify the angle. Check Use the other scale on the protractor to find the measure ofLMN. 130° - 20° = 110°. M

  18. 9-6 Finding Angle Measures in Polygons Course 1 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.

  19. 9-6 Finding Angle Measures in Polygons M J L K Course 1 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°.

  20. 9-6 Finding Angle Measures in Polygons M J L K Caution! Use the scale on the protractor that starts with 0°. Course 1 Additional Example 2 Continued Use the protractor. The measure of the angle is 145°. mK = 145°, so the estimate is reasonable.

  21. 9-6 Finding Angle Measures in Polygons A B D C Course 1 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°.

  22. 9-6 Finding Angle Measures in Polygons A B D C Course 1 Check It Out: Example 2 Continued Use the protractor. The measure of the angle is 53°. mD = 53°, so the estimate is reasonable.

  23. 9-6 Finding Angle Measures in Polygons A B E C D Course 1 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° C= 90°

  24. 9-6 Finding Angle Measures in Polygons A B E C D Course 1 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°. Use a protractor to measure E. E= 135°

  25. 9-6 Finding Angle Measures in Polygons A B C D Course 1 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° A = 70°

  26. 9-6 Finding Angle Measures in Polygons A B C D Course 1 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°. Use a protractor to measure C. C= 110°

  27. 9-6 Finding Angle Measures in Polygons Course 1 Insert Lesson Title Here 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

  28. 9-6 Finding Angle Measures in Polygons Course 1 Insert Lesson Title Here 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. 45°

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