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 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 rotation

$\frac{360^{\circ}}{15}=24^{\circ}$. The angles of rotational symmetry are multiples of $24^{\circ}$. Also, factors of $360^{\circ}$ are possible angles of rotational symmetry.

Step3: Check the options

$12^{\circ}$ is a factor of $360^{\circ}$ and a sub - multiple of the basic angle of rotation ($24^{\circ}$ is $2\times12^{\circ}$). $45^{\circ}$ is not a factor of $360^{\circ}$ divisible by $15$. $72^{\circ}$ is $3\times24^{\circ}$ and $90^{\circ}$ is not a factor of $360^{\circ}$ divisible by $15$.

Answer:

$12^{\circ}$