Question

is the smallest possible rotation that results in the figure being mapped onto itself.

Explanation:

Step1: Count the number of congruent parts

The figure has 12 congruent - looking parts.

Step2: Calculate the angle of rotation

The formula for the smallest angle of rotation that maps a regular polygon (or a figure with rotational symmetry) onto itself is $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of congruent parts. Here, $n = 12$. So, $\theta=\frac{360^{\circ}}{12}=30^{\circ}$.

Answer:

$30^{\circ}$