We are given that the measure of an interior angle of a regular n -gon is 108 and we are asked to find n. The Polygon Angle-Sum Theorem tells us that the sum of the measures of the interior angles of a regular n -gon is given by the following formula.
(n-2)* 180Because all of the angles in a regular polygon are congruent and the measure of one of them is 108, we know that the sum of angles can also be expressed as 108n. Let's equate both expressions.
(n-2)* 180 = 108n
Let's solve it to find n.
