Question

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: Recall the formula for the smallest angle of rotational symmetry

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

Step2: Set up the equation

We are given that the smallest angle of rotational symmetry is \(30^{\circ}\). So, \(\frac{360^{\circ}}{n}=30^{\circ}\).

Step3: Solve for \(n\)

Cross - multiply to get \(n=\frac{360^{\circ}}{30^{\circ}}\).

$$n = 12$$

Answer:

B. 12