Rotational symmetry is when a figure can be rotated by an angle between 0° and 360° and still look the same. The angle of rotational symmetry is the smallest angle that can do this. The only angle of rotational symmetry for all figures is 360°, because it returns the figure to its original position. Any other angle of rotational symmetry depends on the shape of the figure.
For example, a square has a rotational symmetry of order 4 about its center of rotation. Hence, the angle of rotation is 90°. A square is a quadrilateral with all its internal angles measuring 90° each. From the above figure we see that the order of rotational symmetry of a square is 4 as it fits into itself 4 times in a complete 360° rotation.
In general, for any regular polygon with n sides, there are n angles of rotation that give rotational symmetry. These angles are given by 360°/n, 2×360°/n, 3×360°/n,...,(n-1)×360°/n.
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