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).
(..) between the sewer lids... directly under the guillotine platform... noted the loose board under the basket... computed the angle at which the setting sun momentarily blinding the executioner... and chose that moment to swipe the executioner's melon... (..)2014 Mr. Peabody & Sherman