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Finding Angle Measures in Polygons: Understanding and Estimating Angles

This lesson focuses on finding and estimating angle measures in various polygons. Students will learn how to solve equations involving angles, apply the use of protractors, and classify angles based on their measurements. The lesson includes examples such as calculating the third angle of a triangle given two angles and estimating angles in parallelograms. By the end of the course, students will gain confidence in measuring angles accurately and understanding their properties.

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Finding Angle Measures in Polygons: Understanding and Estimating Angles

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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 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°.

  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 • The measure of XYZ is 150°- 70°, or 80°. Write this as mXYZ = 80°.

  7. 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.

  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. Check Use the other scale on the protractor to find the measure ofXYZ. 110° - 30° = 80°. Y

  9. 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.

  10. 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°.

  11. 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.

  12. 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°.

  13. 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.

  14. 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°

  15. 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°

  16. 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°

  17. 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°

  18. 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

  19. 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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