8th Grade Math LESSON 3.2 ANGLES OF TRIANGLES The angles inside a polygon are called interior angles. When the sides of a polygon are extended, other angles are formed. The angles outside the polygon that are adjacent to the interior angles are called exterior angles. DEFINITION The sum of the interior angle measures of a triangle is 180º Key Idea Interior angle measure of a triangle xº yº zº xº yº zº yº zº xº xº zº yº x° 32° x + 32 + 48 = 180 x + 80 = 180 x = 100 48° (x+28)° x° x+(x+28)+90 = 180 2x+118 = 180 2x = 62 x = 31 81 + 25 + x = 180 81° x° 106 + x = 180 25° x = 74 x° (x-35)° 43° x + (x-35) + 43 = 180 2x + 8 = 180 2x = 171 x = 86 The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Key Idea Exterior angle measure of a triangle xº yº zº xº yº zº zº yº xº zº xº yº x° 36° 72° 36 + 72 = x 108 = x 2a = (a - 5) + 80 2a = a + 75 a = 75 80° (a - 5)° 2a° 55 + 50 = x 105 = x 55° x° 50° 32 + 90 = x 122 = x x° 32°