Polygon Interior Angle Sum Theorem Polygon interior angle sum theorem: The sum of Can be divided into 3 triangles the measures of the angles of any -gon is 180(n-2), where n is the number of of M the polygon. What is the sum of the measures of the interior angles of a pentagon? Apentagon has 5 sides, so n = 5. 180(5-2) 180(3) = Using the Polygon Interior Angle Sum Theorem What is the measure of K? Find the sum of all of the interior angles. 1800-2) and n = 6 54 107 106 180(4) 115 154 Find the sum of the angle measures that we know. H M 106 +115 154 +90 + 107 = Subtract this from the total measure of all interior angle. 720-572=