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 sectors

The image (a circular design with alternating blue and yellow sectors) has 12 equal - looking sectors (since the pattern repeats 12 times around the circle).

Step2: Calculate the rotational symmetry angle

For a figure with rotational symmetry, the smallest angle of rotation (the angle by which we can rotate the figure so that it maps onto itself) is given by the formula $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of equal - angle sectors (or the order of rotational symmetry). Here, $n = 12$. So, $\theta=\frac{360^{\circ}}{12}=30^{\circ}$.

Answer:

$30^{\circ}$