A projecting edge
ridge, sharp edge, projection, angle; see edge 1, rim.
niche, nook, indentation; see hole 2, recess 2.
A sharp turn
bend, veer, shift; see curve 1, turn 2.
The angle made where ways intersect
fork, branch, V, Y, intersection, junction, four corners, cloverleaf; see also crossing 1, junction 2.
predicament, impasse, tight spot, hole*; see difficulty 1, 2, predicament.
control, edge, monopolization; see monopoly. See syn. study at monopoly.
around the corner
the (four) corners of the earth
turn the corner