The diagonals of the rectangle ABCD intersect at point O. Find the angle between the diagonals if the angle BAC = 50

The diagonals of the rectangle are equal and at the point of intersection they are divided in half, which means AO = BO, therefore the triangle AOB is isosceles with the base AB, the angles at the base are equal, therefore ∠ BAC = ∠ ABO = 50 °. The sum of the angles of the triangle is 180 °, which means the angle between the diagonals AOB = 180 – ∠ BAC – ∠ ABO = 180 – 50 – 50 = 80 °.