Question

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

Explanation:

Step1: Recall the formula for rotational symmetry angle

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

Step2: Identify \(n\) for an octagon

For a regular octagon, \(n = 8\)

Step3: Calculate the angle

Substitute \(n = 8\) into the formula: \(\frac{360^{\circ}}{8}=45^{\circ}\)

Answer:

45