Question

the regular polygon below is to be rotated about its center. what is the minimum angle of rotation that would carry the figure onto itself? answer 90° 210° 180° 30°

Explanation:

Step1: Determine the number of sides

The polygon is an octagon, so $n = 8$.

Step2: Use the rotation - angle formula

The formula for the minimum angle of rotation $\theta$ of a regular $n$-sided polygon about its center to carry it onto itself is $\theta=\frac{360^{\circ}}{n}$. Substitute $n = 8$ into the formula, we get $\theta=\frac{360^{\circ}}{8}=45^{\circ}$. But among the given options, we know that for an octagon, the next - level non - minimum but still valid rotation angle that is in the options is $90^{\circ}$ (since $90^{\circ}$ is a multiple of the minimum rotation angle $45^{\circ}$).

Answer:

$90^{\circ}$