Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.

Prove that the points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.

Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2 = 0.

Find the angles between pairs of straight lines 3x – y + 5 = 0 and x – 3y + 1 = 0

Find the angles between pairs of straight lines 3x + y + 12 = 0 and x + 2y – 1 = 0