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).
(..) into thinking of making big changes in their system because, We certainly don't want another war like that, do we? There's that fear angle again. And they thought, Well, by being in World War I then we would be a major participant at the table to carve up the world (..)2009 Loose Change 9/11: An American Coup