Question

An interior angle of a regular polygon has a measure of 108°. what type of polygon is it? pentagon hexagon octagon nonagon

Answer 1

$Exterior \ = \ supplement \\ 180-108 = 72 \\ 360/72 = 5 \\ Polygon \ is \ a \ pentagon.$

Answer 2

Answer: Pentagon

Step-by-step explanation:

Since, an interior angle of a regular polygon is,

$\frac{(n-2)\times 180^{\circ}}{n}$

Where n is the number of sides of the polygon,

According to the question,

$\frac{(n-2)\times 180^{\circ}}{n}=108^{\circ}$

$\implies 180n - 360 = 108n$

$\implies 180 n - 108 n = 360$

$\implies 72 n = 360$

$\implies n = 5$

Thus the number of sides of the given regular polygon is 5,

⇒ It is a pentagon.