Question

1 for each figure, identify any angles of rotation that create symmetry.

Explanation:

Step1: Recall the concept of rotational symmetry

A figure has rotational symmetry if it looks the same after a rotation of \(n^{\circ}\) where \(0 < n<360\).

Step2: Analyze the first figure (Yin - Yang symbol)

The Yin - Yang symbol has rotational symmetry of \(180^{\circ}\). If we rotate it by \(180^{\circ}\) around its center, it maps onto itself.

Step3: Analyze the second figure (the cross - like figure)

This figure has rotational symmetry of \(180^{\circ}\). Rotating it by \(180^{\circ}\) around its center makes it coincide with its original position.

Step4: Analyze the third figure (the figure of the person)

This figure has no rotational symmetry (other than \(360^{\circ}\)). There is no angle \(n\) with \(0 < n<360\) such that rotating it by \(n^{\circ}\) around any point makes it look the same.

Answer:

The first figure has a rotation angle of \(180^{\circ}\) for symmetry. The second figure has a rotation angle of \(180^{\circ}\) for symmetry. The third figure has no non - \(360^{\circ}\) rotation angles for symmetry.