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Chapter 11

Chapter 11. Area of Polygons and Circles. Angle Measures in Polygons 11.1. California State Standards 12: find and use side and angle measures of polygons 13: prove polygon angle relationships. investigation. 3. 1. 180 o. investigation. 180 o. 180 o. investigation. 3.

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Chapter 11

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  1. Chapter 11 Area of Polygons and Circles

  2. Angle Measures in Polygons 11.1 California State Standards 12: find and use side and angle measures of polygons 13: prove polygon angle relationships

  3. investigation 3 1 180o

  4. investigation 180o 180o

  5. investigation 3 1 180o 4 2 360o

  6. investigation 180o 180o 180o

  7. investigation 3 1 180o 4 2 360o 5 3 540o

  8. investigation 180o 180o 180o 180o

  9. investigation 3 1 180o 4 2 360o 5 3 540o 6 4 720o n n – 2 180(n – 2)o

  10. theorem • Polygon Interior Angles • The sum of the measures of the • interior angles of a convex polygon is • 180(n – 2)o • n is the number of sides.

  11. 135 114 102 + 105 456 example 114o 102o 135o angles of pentagon 180(3 ) 180(5 – 2 ) 540 105o 84o 540 – 456 = 84 xo

  12. corollary • Regular Polygon Interior Angle • The measure of each interior angle • of a regular polygon is

  13. example • The measure of each interior angle of • a regular polygon is 165o. • How many sides does the polygon have? -360 = -15n 180n – 360 = 165n 180(n – 2) = 165n 24 = n

  14. theorem • Polygon Exterior Angles • The sum of the measures of the • exterior angles of a convex • polygon (one at each vertex) is 360o. 6 1 5 2 4 3

  15. Knott’s Berry Farm A portable ferris wheel in England

  16. Austria - Vienna: Riesenrad - the Giant Wheel at the Prater

  17. example • Find the value of y. yo 2yo 2yo yo 2y + y + 2y + y = 360 6y = 360 y = 60

  18. corollary • Regular Polygon Exterior Angle • The measure of each exterior angle • of a regular polygon is

  19. example • Find the value of x. xo

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