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 equal parts

The orange slice image is divided into 10 equal - sized sectors (triangular - like parts) around the center.

Step2: Calculate the rotation angle

For a figure with rotational symmetry divided into \(n\) equal parts, the smallest angle of rotation (the angle of rotational symmetry) is given by the formula \(\theta=\frac{360^{\circ}}{n}\). Here, \(n = 10\), so \(\theta=\frac{360^{\circ}}{10}=36^{\circ}\).

Answer:

\(36\)