Question

Complete the following statement.

If a regular polygon has 40 sides, the measure of each interior angle is ___?

Short answer

If a regular polygon has 40 sides, then the measure of each interior angle is 171 degrees.

Step-by-step solution

Step 1- Apply the formula of the interior angle.

The measure of each interior angle is$\frac{180(n-2)}{n}$.

Step 2- Find the measure of interior angle.

Here$n=40$.

Substitute 40 for n in the formula and find the interior angle.

Step 2- Step description.

$\begin{array}{l}=\frac{180(n-2)}{n}\\ =\frac{180(40-2)}{40}\\ =\frac{180\left(38\right)}{40}\\ =171\end{array}$.

Therefore, the measure of each interior angle is 171 degrees.