Question

what is the smallest angle of rotational symmetry for the regular octagon?

Explanation:

Step1: Recall rotational - symmetry formula

The formula for the smallest angle of rotational symmetry of a regular polygon is $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of sides of the polygon.

Step2: Identify number of sides of octagon

A regular octagon has $n = 8$ sides.

Step3: Calculate the angle

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

Answer:

$45$