We are given that the measure of an interior angle of a regular n -gon is 135 and we want to find n. The Polygon Interior Angles Sum Theorem tells us that the sum of the interior angle measures of an n-gon is (n-2)180.
Since all angles in a regular polygon are congruent, our regular n-gon has n angles that each have a measure 135. Therefore, the sum of the angle measures equals n times 135.
(n-2)180 = 135n
Let's solve the above equation to find n.
