Question

if the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?
10
12
20
24

Explanation:

Step1: Recall the formula

The smallest angle of rotation $\theta$ of a regular polygon is given by $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of sides.

Step2: Solve for $n$

We know $\theta = 18^{\circ}$, so $n=\frac{360^{\circ}}{\theta}$. Substituting $\theta = 18^{\circ}$, we get $n=\frac{360}{18}=20$.

Answer:

C. 20