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).
(..) Guys, I'm running the numbers, and even with optimal val blow... We're gonna be off on our angle. What's the intercept distance? Johanssen? meters, approximate. That's too far. Commander? (..)2015 The Martian