Chapter 11-Area of Polygons & Circles Angle Measures in Polygons Section 11.1 Goal – To find the measures of interior and exterior angles of polygons.

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Presentation transcript:

Chapter 11-Area of Polygons & Circles Angle Measures in Polygons Section 11.1 Goal – To find the measures of interior and exterior angles of polygons

Vocabulary Review Convex polygon – n- gon – Regular polygon – A polygon that is not concave. A polygon that has many sides; specifically, n. A polygon that is equilateral and equiangular.

Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n – 2)180. Polygon #of sides “n” # of Δ’s sum of int. angles Triangle311 x 180° Quadrilateral422 x 180° Pentagon533 x 180°

Corollary to Theorem 11.1 The measure of each interior angle of a regular n-gon is

Example 102° 105° 135° 114° x°x°

Example

Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon is 360°.

Corollary to Theorem 11.2 If the polygon is a regular n-gon, the measure of each exterior angle is (n = # of sides)

Example 2y° y°y° y°y°

Example y°y°