Question

select the correct answer
a regular polygon has an exterior angle measuring $30^{circ}$. how many sides does the polygon have?
a. 14
b. 8
c. 12
d. 10

Explanation:

Step1: Recall the formula for exterior angles of a regular polygon

The sum of the exterior angles of any regular polygon is \( 360^\circ \). For a regular polygon, each exterior angle is equal. So if we let \( n \) be the number of sides (and also the number of exterior angles), and \( \theta \) be the measure of each exterior angle, then \( n\times\theta = 360^\circ \).

Step2: Solve for the number of sides \( n \)

We know that \( \theta = 30^\circ \). Substituting into the formula \( n=\frac{360^\circ}{\theta} \), we get \( n = \frac{360^\circ}{30^\circ} \).
Calculating \( \frac{360}{30}=12 \).

Answer:

C. 12