The diagonals of rectangle ABCD meet at point O. Find the angle between the diagonals if ABO = 30 °.

Consider the ABO triangle. This triangle is isosceles, according to the problem statement we know the angle at the base, we find the angle AOB at the apex.
∠ AOB = 180 ° – 2 * ∠ABO = 180 ° – 2 * 30 ° = 180 ° – 60 ° = 120.
Angle AOB and angle AOD are adjacent. Let’s find the angle AOD:
∠ AOD = 180 ° – ∠ AOB = 180 ° – 120 ° = 60 °.
The angle AOD is also the outer angle of the triangle AOB:
∠ AOD = ∠ABO + ∠ VAO = 30 ° + 30 ° = 60 °.
Answer: The diagonals intersect at 120 ° and 60 °.