Question

determining sides from angles of rotational symmetry
the smallest angle of rotational symmetry for a regular polygon is 30°. how many sides does the regular polygon
have?
9
12
20
30

Explanation:

Step1: Use the formula for the smallest angle of rotational symmetry

The formula for the smallest angle of rotational symmetry \(\theta\) of a regular polygon with \(n\) sides is \(\theta=\frac{360^{\circ}}{n}\).

Step2: Solve for \(n\)

Given \(\theta = 30^{\circ}\), we substitute into the formula \(30^{\circ}=\frac{360^{\circ}}{n}\). Then \(n=\frac{360^{\circ}}{30^{\circ}}\).

$$n = 12$$

Answer:

12