6.1 The Polygon Angle-Sum Theorem

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Presentation transcript:

6.1 The Polygon Angle-Sum Theorem Boyd/Usilton

Theorem 6-1 Polygon Angle-Sum Theorem The sum of the measures of interior angles of an n-gon is (n-2)180. n= # of sides What is the sum of the interior angles of a heptagon?

Polygons Equilateral: A polygon with all sides congruent. Equiangular: A polygon with all angles congruent. Regular polygon: A polygon that is both equilateral and equiangular.

Corollary to the Polygon Angle-Sum Theorem The measure of each interior angle of a regular n-gon is (n-2)180 n

Theorem 6-2 Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. For pentagon, m<1 + m<2 +m<3 +m<4 +m<5=360