Question

1. what is the angle of rotation of the following figure? 45° 180° 60° 90°

Explanation:

Step1: Analyze the figure's symmetry

The figure (snowflake - like) has 6 identical parts. For a rotational - symmetric figure, the angle of rotation \( \theta \) is given by \( \theta=\frac{360^{\circ}}{n} \), where \( n \) is the number of equal - angle - spaced parts. Here, \( n = 6 \).

Step2: Calculate the angle of rotation

Using the formula \( \theta=\frac{360^{\circ}}{n} \), substitute \( n = 6 \). We get \( \theta=\frac{360^{\circ}}{6}=60^{\circ} \). Also, we can visually check: rotating the figure by \( 60^{\circ} \) will make it coincide with its original position. Rotating by \( 45^{\circ} \), \( 90^{\circ} \) or \( 180^{\circ} \) (without considering the \( 60^{\circ} \) multiple) will not make it match the original figure's orientation as well as a \( 60^{\circ} \) rotation.

Answer:

60° (The option corresponding to 60°)