Question

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

Explanation:

Step1: Recall rotation symmetry concept

Rotation symmetry means a figure looks the same after a rotation. The full - circle rotation is \(360^{\circ}\).

Step2: Analyze the yin - yang symbol

When we rotate the yin - yang symbol by \(180^{\circ}\), the black and white parts (along with their small circles) swap positions in a way that the overall appearance of the symbol remains unchanged. For example, if we consider the center of the circle as the center of rotation, a \(180^{\circ}\) rotation (a half - turn) maps each point \(P(x,y)\) (relative to the center \((h,k)\)) to \(P'(2h - x,2k - y)\). In the case of the yin - yang symbol, this transformation results in the same visual pattern. Rotations of other angles (like \(90^{\circ}\), \(120^{\circ}\) etc.) do not preserve the visual identity of the symbol.

Answer:

The angle of rotation that creates symmetry for the yin - yang symbol is \(180^{\circ}\)