The diagonals of the rectangle ABCD intersect at point O and the angle ABO is 40 ° find the angles between the diagonals.

Since the diagonals of a rectangle are by definition equal and are divided in half at the point of intersection, the triangle AOB is isosceles.

Let us determine the degree value of the angle AOB, which is one of the angles between the diagonals, knowing by the condition of the problem that the angle ABO is 40 °:

180 – (40 + 40) = 100.

Let us determine the degree value of the angle СOB, which is another of the angles between the diagonals and the adjacent angle AOB:

180 – 100 = 80.

Answer: The degree values of the angles formed by the diagonals are equal to 100 ° and 80 °.