a salesman who's always looking for an 'angle' [=looking for a way to convince people to buy the things he is selling]
The two lines meet at a 30-degree 'angle' to each other. = There is a 30-degree 'angle' between the two lines.
The two lines form a sharp 'angle'. = The two lines meet/intersect at a sharp 'angle' (to each other).
(..) I just graduated last spring. What did you study? Philosophy. Yeah, there's a good buck in that racket. Yeah. Well, so far it's pro bono. Well, I'm sure you'll figure out the angles. Yeah. I hope your Porsche works out. Cheers to that, huh? Cheers to that. Kanpai. Wish I could sleep. Me too. (..)2003 Lost in Translation