Question

question which angle of rotation would carry a regular octagon onto itself? answer 225° 300° 252° 330°

Explanation:

Step1: Calculate the central angle

The central angle of a regular octagon is $\frac{360^{\circ}}{8}=45^{\circ}$. A regular octagon will map onto itself when rotated by an angle that is a multiple of the central - angle.

Step2: Check each option

• For $225^{\circ}$, $\frac{225^{\circ}}{45^{\circ}} = 5$, which means 225° is a multiple of 45°.
• For $300^{\circ}$, $\frac{300^{\circ}}{45^{\circ}}=\frac{20}{3}$, not a whole - number.
• For $252^{\circ}$, $\frac{252^{\circ}}{45^{\circ}}=\frac{28}{5}$, not a whole - number.
• For $330^{\circ}$, $\frac{330^{\circ}}{45^{\circ}}=\frac{22}{3}$, not a whole - number.

Answer:

A. $225^{\circ}$