Question

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

Short answer

The measure of each interior angle is $\mathbf{160}\mathbf{°}$.

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 $\frac{\left(n-2\right)\mathbf{180}}{n}$.

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:

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

Step 3. Write the conclusion.

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