Question

what is the smallest angle of rotation about its center that carries a regular hexagon onto itself?

Explanation:

Step1: Recall full rotation angle

A full rotation around a point is $360^\circ$.

Step2: Identify number of sides

A regular hexagon has 6 equal sides/vertices.

Step3: Calculate smallest rotation angle

Divide full rotation by number of sides: $\frac{360^\circ}{6}$

Answer:

$60^\circ$