the measure of each interior angle of a regular polygon is 135. how many sides does the polygon have. explain how you came up with your answer.

Answer 1

The sum of the interior angles of a polygon is (n-2) 180, where n is the number of sides.

In a regular polygon, each of those angles is equal, so each interior angle has a value of:

(n-2)180/n

We are given the interior angle is 135, so we can use the above formula to solve for n.

135 = (n-2)180/n

135n = 180n - 360

-45n = -360

n = 8