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

Looking at the image, we can see that there are 12 blades (or similar repeating parts) in the rotational - symmetric figure.

Step2: Calculate the rotational 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 times the figure can be rotated to coincide with itself (or the number of equal - angled sectors we can divide the full - circle rotation into). Here, $n = 12$. So we calculate $\theta=\frac{360^{\circ}}{12}$.
$\frac{360^{\circ}}{12}=30^{\circ}$

Answer:

$30$