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).
(..) - The name stays. Right, well, then the new trick's gonna have to be irresistible then. I have a couple of methods to try out. And then we need a new angle on the presentation. And if you need some inspiration, there's a technical exposition at the Albert Hall this week. (..)2006 The Prestige