The diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n′ = 0, mx + ly + n = 0, mx + ly + n′ = 0 include an angle

Since the distance between the parallel lines lx + my + n = 0 and lx + my + n′ = 0 is same as the distance between the parallel lines mx + ly + n = 0 and mx + ly + n′ = 0. Therefore, the parallelogram is a rhombus. Since the diagonals of a rhombus are at right angles, therefore the required angle is π2.