The diagonals of rectangle ABCD intersect at point o find the angle between the diagonals if the angle ABO is 30 degrees.

If the ABO angle is 30 degrees, then the opposite ABO angle is also 30 degrees. A rectangle is a symmetrical figure, its diagonals are equal to each other, the corners are symmetrical.
Consider the triangle AOB, the two angles of which we already know. The sum of all the angles of the triangle must be 180 degrees. Find the third angle AOB:
180 – 30 – 30 = 120 degrees.
The diagonals intersect at an angle of 120 degrees. The second acute intersection angle will be:
180 – 120 = 60 degrees.