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

The formula for the smallest angle of rotational symmetry $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of times the figure matches itself in a full - 360 - degree rotation.

Step2: Determine the value of n

The flower - shaped figure matches itself 5 times in a 360 - degree rotation, so $n = 5$.

Step3: Calculate the angle

$\theta=\frac{360^{\circ}}{5}=72^{\circ}$

Answer:

$72^{\circ}$