Question

a regular polygon has 15 sides. which is a possible angle of rotational symmetry for the figure? 12° 45° 72° 90°

Explanation:

Step1: Recall rotation - symmetry formula

The formula for the angle of rotational symmetry of a regular polygon is $\frac{360^{\circ}}{n}$, where $n$ is the number of sides of the polygon, and also any factor of $\frac{360^{\circ}}{n}$ is an angle of rotational symmetry.

Step2: Calculate $\frac{360^{\circ}}{n}$ for $n = 15$

$\frac{360^{\circ}}{15}=24^{\circ}$.

Step3: Check the factors

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Among the given options, 12° is a factor of 24°, while 45°, 72°, and 90° are not factors of 24°. So 12° is a possible angle of rotational symmetry.

Answer:

A. 12°