The diagonals of the rectangle ABCD intersect at the point O, and the perpendicular BE drawn to the diagonal AC makes

The diagonals of the rectangle ABCD intersect at the point O, and the perpendicular BE drawn to the diagonal AC makes an angle of 40 ° with the diagonal BD. calculate the angles between the diagonals.

Consider a BOE triangle in this rectangle, angle E = 90 degrees:
Since the sum of the angles of a triangle is 180, then
BOE angle = 180-90-40 = 50 degrees = BOA angle.
Since to the BOD-unfolded angle, then it is equal to 180 degrees, the BOA angle = 50 degrees, then the AOD angle = 180-50 = 130 degrees.
Angle BOA = angle COD and angle BOC = angle AOD by the property of a rectangle, therefore angle BOA = angle COD = 50 degrees and angle BOC = angle AOD = 130 degrees.