Question

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

Explanation:

Step1: Recall the definition of rotational symmetry

A figure has rotational symmetry if it looks the same after a rotation of \(x^{\circ}\) (where \(0 < x<360\)). But if we rotate a figure by \(360^{\circ}\), every figure (by the nature of rotation, a full - turn rotation) will map onto itself.
For example, consider a triangle. A non - equilateral triangle may have rotational symmetry of \(360^{\circ}\) (since after a full rotation it looks the same). For a square, it has rotational symmetries of \(90^{\circ},180^{\circ},270^{\circ},360^{\circ}\). But for a general irregular polygon (or any irregular 2D shape), the only guaranteed rotational symmetry angle (because of the definition of rotation: rotating a figure by \(360^{\circ}\) brings it back to its original position) is \(360^{\circ}\).

Answer:

\(360^{\circ}\)