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: Determine the number of identical parts

The flower has 8 identical parts.

Step2: Calculate the rotation angle

The full rotation is \(360^{\circ}\). To find the smallest rotation angle \(\theta\) for the image to look the same, use the formula \(\theta=\frac{360^{\circ}}{n}\), where \(n\) is the number of identical parts. Here \(n = 8\), so \(\theta=\frac{360^{\circ}}{8}\).
$$\frac{360^{\circ}}{8}=45^{\circ}$$

Answer:

\(45\)