Answer to Question #33614 in Trigonometry for Lawrence

Question

Hi. This is the question:
A jet flew 140 mi on a course of 196 degrees and then 120 mi on a course of 106 degrees then the jet return to its starting point via the shortest route possible. Find the total distance that the jet traveled.
I found the answer for this. It's this one:
http://ph.answers.yahoo.com/question/index?qid=20110828043233AAVgQcy
Now I understand everything else, ut my problem is why they used the given angles to confirm that it is a right triangle? I know this has something to do with theorems on parallel lines, but I just can't to picture how. Illustrations are greatly appreciated. (It will actually be a lot easier for me to understand this question). Thank you.