Question

question 24 of 40 each exterior angle of a regular polygon measures 45°. how many sides does the polygon have? a. 8 b. 15 c. 12 d. 10

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 $\theta = 45^{\circ}$, we have $n=\frac{360^{\circ}}{\theta}$. Substituting $\theta = 45^{\circ}$ into the formula, we get $n=\frac{360}{45}=8$.

Answer:

A. 8