Question

if the smallest angle of rotation for a regular polygon is 18°, how many sides does the polygon have?
8
10
20
36

Explanation:

Step1: Recall the formula for angle of rotation

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

Step2: Solve for \(n\)

We know \(\theta = 12^{\circ}\), so from \(\theta=\frac{360^{\circ}}{n}\), we can rewrite it as \(n=\frac{360^{\circ}}{\theta}\). Substituting \(\theta = 12^{\circ}\) into the formula, we get \(n=\frac{360}{12}=30\).

Answer:

30