In the rectangle ABCD, the diagonals AC and BD intersect at the point O. Angle ABO = 40.

In the rectangle ABCD, the diagonals AC and BD intersect at the point O. Angle ABO = 40. Find the angles between the diagonals of the rectangle AOB and BOC.

The diagonals in the rectangle, by their intersection, form four isosceles triangles, which are equal in pairs. Consider one of them – the ABO triangle, in which we know the angle at the base. Let’s find the angle AOB at the vertex of this triangle. The same angle will be one of the angles between the diagonals of the rectangle.
∠ AOB = 180 ° – 2 * ∠ ABO = 180 ° – 2 * 40 ° = 100 °.
Let’s find the angle BOS, it is an adjacent angle with AOB.
∠ BОС = 180 ° – ∠ AOB = 180 ° – 100 ° = 80 °.
Answer: the AOB angle is 100 °, the BOC angle is 80 °.