Question

23 each exterior angle of a regular polygon has a measure of 30°. what is the total number of sides of the polygon? a 6 b 9 c 12 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 \(30^{\circ}\), we use the formula \(n=\frac{360^{\circ}}{\text{measure of one exterior angle}}\). So \(n = \frac{360}{30}\).

$$n=\frac{360}{30}=12$$

Answer:

C. 12