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: Analyze the image's symmetry

The image (a window with shutters) is symmetric about 180° rotation. A 180° rotation will map the top - bottom and left - right parts appropriately to make it look the same. For a figure with rotational symmetry, the smallest angle of rotation (rotational symmetry order related) for this window - like figure (which is symmetric in a way that 180° rotation aligns it) is 180 degrees.

Step2: Confirm the rotation angle

Since the figure is symmetric such that rotating it 180° around its center will result in the same appearance (the shutters and window panes will align), the smallest number of degrees is 180.

Answer:

180