Question

An interior angle of a regular polygon has a measure of 108. What type of polygon is it?

Answer 1

Answer:

pentagon

Step-by-step explanation:

Recall that for any regular polygon, the number of sides and the interior angles are related through the following formula.

Interior Angle, θ = 180(n-2) / n  ; where n is the number of sides

Rearranging :

θ = 180(n-2) / n

nθ = 180 (n-2)

nθ = 180n - 2(180)

nθ = 180n - 360

180n - nθ = 360

n(180 - θ) = 360

n = 360 / (180 - θ)  (given that θ = 108°)

n = 360 / (180 - 108)

n = 5

since the polygon has 5 sides, it is a pentagon

Answer 2

Answer:

pentagon

Step-by-step explanation: