Question

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 exterior - angle formula

The sum of exterior angles of any polygon is $360^{\circ}$. For a regular polygon with $n$ sides, each exterior angle $\theta=\frac{360^{\circ}}{n}$.

Step2: Solve for $n$

Given $\theta = 30^{\circ}$, we have $n=\frac{360^{\circ}}{\theta}$. Substituting $\theta = 30^{\circ}$ into the formula, we get $n=\frac{360}{30}=12$.

Answer:

C. 12