Question

how many degrees of rotational symmetry does this octagon have that would allow it to map back onto itself?
90 degrees
45 degrees
60 degrees
30 degrees

Explanation:

Step1: Recall rotational - symmetry formula

For a regular \(n\) - sided polygon, the angle of rotational symmetry \(\theta=\frac{360^{\circ}}{n}\).

Step2: Identify \(n\) for an octagon

An octagon has \(n = 8\) sides.

Step3: Calculate the angle of rotational symmetry

\(\theta=\frac{360^{\circ}}{8}=45^{\circ}\)

Answer:

45 degrees