Question

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

Answer 1

The polygon is a penthagon.

In a regular polygon with n sides, the sum of the interior angles is

$180(n-2)$

But we also know that each interior angle has a measure of 108, and of course there is a total of n angles. So, we also know that the sum of the interior angles is

$108n$

Since we have two expressions for the same quantity, these expressions must equal each other:

$180(n-2) = 108n$

To solve for n, let's start by expanding the left hand side:

$180n-360 = 108n$

Now move all terms involving n to the left hand side, and all constants to the right hand side:

$180n-108n = 360$

Simplify the right hand side:

$72n = 360$

And finally, divide both sides by 72:

$n = \frac{360}{72} = 5$

Answer 2

Answer:

A pentagon

Step-by-step explanation:

I got it right on edg.

:)