Reflecting in Intersecting Planes

rotate blue-green plane

rotate green-red plane

intersection
blue-to-green lines
green-to-red lines
arcs

Reflect the blue figure in the blue-green plane to form the green image. Reflect the green figure in the green-red plane to form the red image. The red figure, being reflected twice, is oriented like the blue figure.

Ignoring the green figure, the result of the two reflections is to rotate the blue figure to the red figure about the intersection of the two mirror planes through twice the angle between them.