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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 – A polygon that is not concave. n- gon – A polygon that has many sides; specifically, n. Regular polygon – A polygon that is equilateral and equiangular. Polygon Interior Angles Theorem - 11.1 The sum of the measures of the interior angles of a convex n-gon is (n – 2)180. m(int angles convex polygon) n 2 180 Polygon #of sides “n” # of Δ’s sum of int. angles Triangle 3 1 1 x 180° Quadrilateral 4 2 2 x 180° Pentagon 5 3 3 x 180° Corollary to Theorem 11.1 The measure of each interior angle of a regular n-gon is 180( n 2) n Example Find x: 114° 105° x° 135° 102° Example The meausre of each interior angle of a regular polygon is 140. How many sides does this polygon have? Polygon Exterior Angles Theorem - 11.2 The sum of the measures of the exterior angles of a convex polygon is 360°. 2 1 3 5 4 m1 m2 m3 m4 m5 360 Corollary to Theorem 11.2 If the polygon is a regular n-gon, the measure of each exterior angle is 360 (n = # of sides) n Example Find: y 2y° y° y° 2y° Example Find: y y° Example The meausre of each interior angle of a regular n-gon is 144. Find n, the number of sides.