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

$12^{\circ}$ is not a multiple of $24^{\circ}$.
$45^{\circ}$ is not a multiple of $24^{\circ}$.
$72^{\circ}=24^{\circ}\times3$.
$90^{\circ}$ is not a multiple of $24^{\circ}$.

Answer:

$72^{\circ}$