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 $\theta$) for which the figure looks the same is given by the formula $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of equal - angled sectors (or in the case of a fan - like figure with blades, the number of blades which are symmetrically placed). Here, $n = 8$. So we calculate $\theta=\frac{360^{\circ}}{8}=45^{\circ}$.

Answer:

$45^{\circ}$