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 rotational - symmetry formula

The angle of rotational symmetry of a regular polygon is given by $\frac{360^{\circ}}{n}$, where $n$ is the number of sides, and its multiples. Here, $n = 15$.

Step2: Calculate the basic angle of rotational symmetry

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

Step3: Check the given options for multiples of 24°

We need to find which of the given angles is a multiple of 24°.

• For 12°, $\frac{24}{12}=2$, 12° is a factor of 24°, and $2\times12^{\circ}=24^{\circ}$.
• For 45°, $\frac{45}{24}=\frac{15}{8}$, not a whole - number.
• For 72°, $\frac{72}{24}=3$, 72° is a multiple of 24°.
• For 90°, $\frac{90}{24}=\frac{15}{4}$, not a whole - number.

Answer:

A. 12°