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: Recall rotational - symmetry formula

For a regular polygon with \(n\) sides, the smallest angle of rotation \(\theta\) for which it looks the same is given by \(\theta=\frac{360^{\circ}}{n}\).

Step2: Identify the number of sides

The given polygon is an octagon, so \(n = 8\).

Step3: Calculate the angle of rotation

\(\theta=\frac{360^{\circ}}{8}=45^{\circ}\)

Answer:

45