Question

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

Explanation:

Step1: Recall the formula

The formula for the smallest angle of rotational symmetry of a regular \(n\) - sided polygon is \(\theta=\frac{360^{\circ}}{n}\).

Step2: Identify \(n\) for 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:

\(45^{\circ}\)