Question

If the measures of each interior angle of a regular polygon is 108, then the polygon is $a\left(n\right)$_?_.

Short answer

If the measures of each interior angle of a regular polygon is 108, then the polygon ispentagon.

Step-by-step solution

Step 1. Find the formula that can be used to calculate the interior angle of a regular polygon.

The interior angle of a regular polygon with $n$ sides is $\frac{180\left(n-2\right)}{n}$.

Step 2. Calculate the number of sides (n) by using the formula.

Equate the formula with the given information,

$\begin{array}{c}\frac{180\left(n-2\right)}{n}=108\\ 180n-360=108n\\ 180n-108n=360\\ 72n=360\\ n=\frac{360}{72}\\ =5\end{array}$

Step 3. to find the type of polygon determined by n number of sides.

The number of sides $n=5$. Therefore, the polygon is a pentagon.