Formula for angle between 2 lines

Hi ---

I can't figure out the yellow and red
parts of the solution to the problem below.

That picture at the bottom is mine. I drew it to try to help me but I am still
confused.

http://img833.imageshack.us/img833/6334/11201.jpg

Yellow: Where did they get from? Why
do we care about this?

Red: If why is ?

Thanks a lot ---

Yellow - You have it marked. Your is nicely labeled. What would you label the next angle - continuing anti-clockwise? It begins on your blue ray and ends with the portion of the red ray extended through the origin.

Red - This is just a second case. If you changed to 160º, would give an acute angle?