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 $\displaystyle 180 - (\theta_2 - \theta_1)$ from? Why

do we care about this?

**Red:** If $\displaystyle \theta_2 < \theta_1$ why is $\displaystyle \alpha = 180 - (\theta_2 - \theta_1)$?

Thanks a lot ---

Re: Formula for angle between 2 lines

Yellow - You have it marked. Your $\displaystyle \theta_{1} - \theta_{2}$ 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 $\displaystyle \theta_{1}$ to 160º, would $\displaystyle \theta_{1} - \theta_{2}$ give an acute angle?