The composition of two inverse orthogonal maps is a direct orthogonal map.

Therefore. the composition of two symmetries with respect to two lines in the plane is a rotation. Specifically, the angle of rotation is twice the angle formed by the axes.

You can verify this fact by modifying the axes 1 and 2 of symmetry that appear in the drawing. Observe how the triangle image by the two symmetries is obtained from the initial triangle by means of the rotation indicated above.

Try to prove this property formally.