Exercise 63 Page 627

We are given that the measure of an interior angle of a regular $n\text{-}$gon is $135.$ The Polygon Interior Angles Sum Theorem tells us that the sum of the interior angle measures of an $n\text{-}$gon is $(n-2)180.$ Since all angles in a regular polygon are congruent, our regular $n\text{-}$gon has $n$ angles with the measure of $135.$ Thus, the sum of the angle measures equals $n$ times $135.$