The angle of rotational symmetry is simply explained as the angle that the figure must cover in order to replicate its current position.
For the given figure, a rotation once would be a ninety degree turn and, after that the figure would be lying on its longer side (that is, the right or left side).
Another ninety degree turn would immediately put the figure upside down and that would be a reflection of its current position.
Note that the figure would need to be rotated twice (two ninety degree turns/rotations).
Therefore, the angle of rotational symmetry is 180 degrees