Question

rotational symmetry does the figure have rotational symmetry? if so, state the degree measure of the angle of rotation. yes no 45° 90° 30° 180°

Explanation:

Step1: Recall rotation - symmetry concept

A regular octagon has rotational symmetry. The formula to find the angle of rotation for a regular polygon is $\frac{360^{\circ}}{n}$, where $n$ is the number of sides.

Step2: Calculate the angle of rotation

For an octagon, $n = 8$. So, $\frac{360^{\circ}}{8}=45^{\circ}$. Also, multiples of this angle like $90^{\circ}(45^{\circ}\times2)$, $180^{\circ}(45^{\circ}\times4)$ will also make the octagon coincide with itself.

Answer:

YES
$45^{\circ}$, $90^{\circ}$, $180^{\circ}$