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 symmetry order

The image is symmetric across its vertical axis, and when rotated 180 degrees, the top and bottom, left and right align perfectly. The full rotation is 360 degrees.

Step2: Calculate smallest rotation

Divide full rotation by the number of times the image maps to itself. For this image, it maps to itself twice in a full rotation (0° and 180°).
$\frac{360^\circ}{2} = 180^\circ$

Answer:

$180^\circ$