Question

this image has rotational symmetry. what is the smallest number of degrees you need to rotate the image for it to look the same?

Explanation:

Step1: Count the number of blades

The fan - like image has 8 blades.

Step2: Calculate the rotational symmetry angle

For a figure with rotational symmetry, the smallest angle of rotation (let's call it $\theta$) that maps the figure onto itself is given by the formula $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of equal - sized parts (in this case, the number of blades). Here, $n = 8$. So we calculate $\theta=\frac{360^{\circ}}{8}$.
$\frac{360^{\circ}}{8}=45^{\circ}$

Answer:

$45$