Question

each exterior angle of a regular polygon measures 15°. how many sides does the polygon have?
a. 24
b. 8
c. 10
d. 15

Explanation:

Step1: Recall the formula for the sum of exterior angles

The sum of exterior angles of any polygon is \(360^{\circ}\).

Step2: Calculate the number of sides

Let \(n\) be the number of sides. Since each exterior angle is \(15^{\circ}\), we use the formula \(n=\frac{360^{\circ}}{\text{measure of one exterior angle}}\). So \(n = \frac{360}{15}\).

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

Answer:

A. 24