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 equal - parts

The gear - like shape has 3 equal parts.

Step2: Use the formula for rotational symmetry

The formula to find the angle of rotational symmetry is $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of equal parts. Here, $n = 3$.
So, $\theta=\frac{360^{\circ}}{3}=120^{\circ}$.

Answer:

$120$