Exercise 62 Page 627

We are given that the measure of an interior angle of a regular n -gon is 108. 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 of 108. Therefore, the sum of the angle measures equals n times 108. (n-2)180 = 108n Let's solve this equation to find n. Knowing the value of n we will be able to identify the polygon.

(n-2)180 = 108n

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Solve for n

Distr

Distribute 180

180n-360=108n

AddEqn

LHS+360=RHS+360

180n=108n+360

SubEqn

LHS-108n=RHS-108n

72n=360

DivEqn

.LHS /72.=.RHS /72.

n=5

Since the polygon has 5 sides, it is a pentagon.