6 1 Polygon AngleSum Theorems CP Geometry Mr

6 -1: Polygon Angle-Sum Theorems CP Geometry Mr. Gallo

Shapes for the next page. Draw all the diagonals possible from only one vertex. Use the information in the chart on the next page.

Find the measures of the interior angles of the following polygons. Complete the table below. Use the shapes on the previous page. Sum of Interior Angle Measures Polygon # of Sides # of s Formed Quadrilateral 4 2 2*180=360 Pentagon 5 3 3*180=540 Hexagon 6 4 4*180=720 Heptagon 7 5 5*180=900 Octagon 8 6 6*180=1080

Polygon Angle-Sum Theorem �The sum of the measures of the interior angles of an ngon is: Examples: Find the sum of the measures of the following polygons: a). Decagon b). 15 -gon c). dodecagon Complete Got It? #1 p. 353 a. 2700

Find the value of x in each polygon. V 122° U 121° 117° T W x° 120° R 118° S Q 82° P 129° T x° 118° 86° S R

Types of Polygons Equilateral Polygon Equiangular Polygon Regular Polygon Corollary to the Polygon Angle-Sum Theorem The measure of each interior angle of a regular n-gon is: Complete Got It? #2 p. 354

Exteriors Angle of a Polygon Find the sum of the exterior angles, one from each vertex of the following polygons. 90° 86° 94° 110° 70° 164° 115° 65° 75° 100° 80°

Polygon Exterior Angle Sum Theorem �The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. 2 1 3 5 4 Complete Got It? #4 p. 355

Homework: p. 356 #18 -25, 29 -36, 41