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

Explanation:

Since, an interior angle of a regular polygon is,

`((n-2)* 180^(\circ))/(n)`

Where n is the number of sides of the polygon,

According to the question,

`((n-2)* 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.