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2.7

2.7. What If It Is An Exterior Angle? Pg. 24 Central and Exterior Angles of a Polygon. 2.7 – What If It Is An Exterior Angle?_____ Central and Exterior Angles of a Polygon

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2.7

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  1. 2.7 What If It Is An Exterior Angle? Pg. 24 Central and Exterior Angles of a Polygon

  2. 2.7 – What If It Is An Exterior Angle?_____ Central and Exterior Angles of a Polygon In the last section, you discovered how to determine the sum of the interior angles of a polygon with any number of sides. But what more can you learn about a polygon? Today you will focus on the interior and exterior angles of regular polygons.

  3. x x x x x x 2.34 – EXTERIOR ANGLES a. Examine the following pictures. With your team find the measure of each exterior angle shown. Then add the exterior angles up. What do you notice?

  4. 38° 98° 71° 67° 86° 360° Sum exterior = ____________

  5. 65° 30° 90° 75° 45° 55° 360° Sum exterior = ____________

  6. 180(6 – 2) 6 = 120° 60° 60° 120° 60° 60° 60° 60° 360° Sum exterior = ____________

  7. http://www.cpm.org/flash/technology/externalangles.swf

  8. b. Compare your results from part (a). As a team, complete the conjectures below. The sum of the exterior angles of a polygon always adds to _____________. Each exterior angles of a regular polygon is found by _____________. 360° 360° n

  9. 2.35 – MISSING ANGLES Find the value of x.

  10. x + 86 + 59 + 96 + 67 = 360 x + 308 = 360 x = 52°

  11. 2x + 59 + 54 + x + 80 + 59 = 360 3x + 252 = 360 3x = 108 x = 36°

  12. 2.36 – USING INTERIOR AND EXTERIOR ANGLES Use your understanding of polygons to answer the questions below, if possible. If there is no solution, explain why not.

  13. Find the measure of each exterior angle of the regular polygon. 12 sides 5 sides 360 12 360 5 = 30° = 72°

  14. Find the number of sides of the regular polygon given the measure of each exterior angle. 60° 24° 360 60 360 24 =6sides = 15

  15. 2.36 –INTERIOR VS EXTERIOR ANGLES a. What is the relationship between interior and exterior angles? Interior + Exterior = 180°

  16. b. Given the interior angle, find the exterior angle. 60° 150° 180° – 60° = 180° – 150° = 120° 30°

  17. Find the number of sides in a regular polygon if each interior angle has the following measures. 108° 135° 144°

  18. 108° (interior) 72° (exterior) 180-108 = 360 72 = 5 sides

  19. 135° (int) 45° (ext) 180-135 = 360 45 = 8 sides

  20. 144° (int) 36° (ext) 180-144 = 360 36 = 10 sides

  21. 2.36 – CENTRAL ANGLES Central angles are located at the center of the polygon. a. What is the relationship between each central angle? What do they add up to? Each angle is congruent Add to 360°

  22. b. Find the measure of the central angle for each polygon.

  23. 360 5 360 8 = 72° 360 6 = 45° = 60°

  24. c. Find the measure of the central angle for each polygon. Octagon Dodecagon 360 12 360 8 = 30° = 45°

  25. 2.37 – CONCLUSIONS Complete the chart with the correct formulas needed to find the missing angles.

  26. 180(n – 2) 360° 360° n 180(n – 2) n

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