Question

the regular polygon below is to be rotated about its center. which angle of rotation would carry the figure onto itself? answer 225° 180° 210° 135°

Explanation:

Step1: 求正六边形最小旋转角

正\(n\)边形绕中心旋转\(\frac{360^{\circ}}{n}\)的整数倍能与自身重合，此为正六边形，\(n = 6\)，则最小旋转角为\(\frac{360^{\circ}}{6}=60^{\circ}\)。

Step2: 分析选项

看哪个选项是\(60^{\circ}\)的整数倍，\(180^{\circ}\div60^{\circ}=3\)，\(180^{\circ}\)是\(60^{\circ}\)的整数倍，而\(225^{\circ}\div60^{\circ}=3.75\)，\(210^{\circ}\div60^{\circ}=3.5\)，\(135^{\circ}\div60^{\circ}=2.25\)，都不是\(60^{\circ}\)的整数倍。

Answer:

\(180^{\circ}\)