Question

question which angle of rotation would carry a regular octagon onto itself? answer 36° 90° 144° 324°

Explanation:

Step1: 求正八边形的中心角

正\(n\)边形的中心角公式为\(\theta=\frac{360^{\circ}}{n}\)，对于正八边形，\(n = 8\)，则\(\theta=\frac{360^{\circ}}{8}=45^{\circ}\)。

Step2: 确定能使正八边形旋转后与自身重合的角度

正八边形绕中心旋转的角度是中心角的整数倍时能与自身重合。\(90^{\circ}\div45^{\circ}=2\)，\(90^{\circ}\)是\(45^{\circ}\)的整数倍；\(36^{\circ}\div45^{\circ}=\frac{4}{5}\)，\(36^{\circ}\)不是\(45^{\circ}\)的整数倍；\(144^{\circ}\div45^{\circ}=\frac{16}{5}\)，\(144^{\circ}\)不是\(45^{\circ}\)的整数倍；\(324^{\circ}\div45^{\circ}=\frac{36}{5}\)，\(324^{\circ}\)不是\(45^{\circ}\)的整数倍。

Answer:

\(90^{\circ}\)