Polygon Exterior Angle Sum Theorem Polygon exterior angle sum theorem The sum of the of the exterior angles of a one ateach vertex is 360 What is the measure of each exterior angle in a regular pentagon Method 1 There are 5 congruentexterior angles 360 Method 2 Use linear pairs 5 Each interior angle has a measure of 108 Using linear pairs we can subtract from 180 180 108 Using the Polygon Exterior Angle Sum Theorem What is the unknown angle measure What is the value of x The sum of the measures of the external angles is 360 90 72 96 82 polygon 360 340 The unknown angle is 20 x 7 20 82 2 linear pair 1 180 3 72 96 5