Question

which angle of rotation is an angle of rotational symmetry for all figures?
45°
90°
180°
360°

Explanation:

Step1: Recall the concept of rotational symmetry

A figure has rotational symmetry if it looks the same after a rotation of \(0 < \theta\leq360^{\circ}\). The full - rotation angle is \(360^{\circ}\). When a figure is rotated by \(360^{\circ}\), it always maps onto itself.
For \(45^{\circ}\), not all figures (e.g., a non - octagonal regular polygon) will have \(45^{\circ}\) as a rotational symmetry angle. For \(90^{\circ}\), non - square or non - rectangle (in some cases) figures may not have \(90^{\circ}\) rotational symmetry. For \(180^{\circ}\), some figures (e.g., equilateral triangle) do not have \(180^{\circ}\) rotational symmetry.

Answer:

\(360^{\circ}\)