Question

the figure below has rotational symmetry. ° is the smallest possible rotation that results in the figure being mapped onto itself.

Explanation:

Step1: Count the number of congruent parts.

The figure has 8 congruent - looking parts.

Step2: Calculate the angle of rotation.

The formula for the smallest angle of rotational symmetry $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of congruent parts. Here $n = 8$, so $\theta=\frac{360^{\circ}}{8}=45^{\circ}$.

Answer:

$45$