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 (the flower can be considered as a regular - shaped object with equal parts), the formula for the smallest angle of rotational symmetry $\theta$ is $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of equal parts or petals.

Step2: Count the number of petals

The flower has 8 petals, so $n = 8$.

Step3: Calculate the angle

Substitute $n = 8$ into the formula: $\theta=\frac{360^{\circ}}{8}=45^{\circ}$.

Answer:

$45$