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Chapter 11 Area of Polygons and Circles

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

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investigation polygon # of sides # of triangles sum of interior angles’ measures Triangle Quadrilateral Pentagon Hexagon n-gon 31 180 o

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investigation 180 o

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investigation polygon # of sides # of triangles sum of interior angles’ measures Triangle Quadrilateral Pentagon Hexagon n-gon 31 180 o 42360 o

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investigation 180 o

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investigation polygon # of sides # of triangles sum of interior angles’ measures Triangle Quadrilateral Pentagon Hexagon n-gon 31 180 o 42360 o 53540 o

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investigation 180 o

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polygon # of sides # of triangles sum of interior angles’ measures Triangle Quadrilateral Pentagon Hexagon n-gon investigation 31 180 o 42360 o 53540 o 64720 o n n – 2180(n – 2) o

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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.

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

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

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

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

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Knott’s Berry Farm A portable ferris wheel in England

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

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example Find the value of y.y. 2yo2yo yoyo 2yo2yo yoyo 2y + y + 2y + y = 360 6y = 360 y = 60

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

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example Find the value of x.x. xoxo

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A polygon is a closed figure whose sides are line segments that intersect only at their endpoints. In a regular polygon , all the angles have the same.

A polygon is a closed figure whose sides are line segments that intersect only at their endpoints. In a regular polygon , all the angles have the same.

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