Reflections over 2 intersecting lines...Another way to represent this transformation?

1) Imagine what Triangle ABC would look like reflected over the x-axis first, and then over the y-axis second.
2) Click to add in the Points A' B' C' and A'' B'' C'' to confirm your idea
3) Think of what kind of OTHER TRANSFORMATION would get you from A -> A'', B --> B'', C -> C''
4) Click to add in the triangles poly1' and poly1'' to confirm your idea
5) Click to add in all the missing segments, including f and g.
6) Click to add in the missing angle, beta.
7) Click the arrow tool in the upper-left, and drag around Point F, adjusting the angle. Look at angle alpha, which is the angle between the 2 intersecting lines that we reflected over, and angle beta, which is the angle of rotation from A to A''. How are they related?