Question

A regular polygon has 18 sides. Find the measure of each interior angle.

Short answer

The measure of each interior angle is160°.

Step-by-step solution

Step 1. Write the formula to find the measure of each interior angle for a regular polygon with n sides.

The formula to find the measure of each interior angle for a regular polygon with n sides is $\frac{\left(n-\mathbf{2}\right)\mathit{180}\mathit{°}}{n}$.

Step 2. Calculate the measure of each interior angle for a regular polygon having 18 sides.

The number of sides in the polygon is 18.

Therefore, the value of n is 18.

Therefore, the measure of each interior angle for a regular pentagon having 18 sides is given by :

$\begin{array}{c}\frac{\left(18-2\right)180}{18}=\frac{16\times 180}{18}\\ =16\times 10\\ =160\end{array}$

Step 3. Write the conclusion.

Therefore, the measure of each interior angle for a regular polygon having 18 sides is 160°.