Question

the figure below has rotational symmetry. 30° is the smallest possible rotation that results in the figure being mapped onto itself.

Explanation:

Step1: Recall rotation - symmetry formula

For a figure with rotational symmetry, the smallest angle of rotation $\theta$ that maps the figure onto itself is given by $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of times the figure can be rotated onto itself in a full - turn ($360^{\circ}$).

Step2: Count the number of congruent parts

Count the number of congruent parts in the given figure. There are 12 congruent parts. So, $n = 12$.

Step3: Calculate the angle of rotation

Substitute $n = 12$ into the formula $\theta=\frac{360^{\circ}}{n}$. We get $\theta=\frac{360^{\circ}}{12}=30^{\circ}$.

Answer:

$30^{\circ}$