Exercise 63 Page 627

We are given that the measure of an interior angle of a regular n -gon is 135. 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 with the measure of 135. Thus, the sum of the angle measures equals n times 135. (n-2)180 = 135n Let's solve the above equation to find n. Knowing the value of n we will be able to identify the polygon.

Since the polygon has 8 sides, it is a octagon.