We know that there are two types of orthogonal transformations in the plane:

- rotations (direct transformations).

- symmetries (inverse transformations).

The composition of a direct and an inverse transformation is an inverse transformation. Therefore the composition  of a rotation and a symmetry is necessarily a symmetry.

You can observe this fact in the figure. The composition of a rotation of angle A and a symmetry respect to the s axis is a symmetry about the s' axis.

Modify the angle of rotation and the initial axis of symmetry s, and study which is the new axis of symmetry that is obtained. Try to make a hypothesis about the relationship between s', s, and A. Prove it.