Question

A regular polygon has 24 sides. Find the measure of each exterior angle.

Short answer

The measure of each exterior angle is $\mathbf{15}\mathbf{°}$.

Step-by-step solution

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

The formula to find the measure of each exterior angle for a regular polygon with sides$n$ is $\frac{360}{n}$.

Step 2. Calculate the measure of each exterior angle for a regular polygon having 24 sides.

The number of sides in the polygon is 24.

Therefore, the value of$n$ is 24.

Therefore, the measure of each exterior angle for a regular pentagon having 24 sides is given by:

$\frac{360}{24}=15$

Step 3. Write the conclusion.

Therefore, the measure of each exterior angle for a regular polygon having 24 sides is $15°$.