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: Identify the number of rotational symmetries

The image has 4 - fold rotational symmetry.

Step2: Calculate the angle of rotation

A full - rotation is 360 degrees. For an object with $n$ - fold rotational symmetry, the smallest angle of rotation $\theta$ is given by $\theta=\frac{360^{\circ}}{n}$. Here $n = 4$. So $\theta=\frac{360^{\circ}}{4}=90^{\circ}$.

Answer:

$90^{\circ}$