The diagonals of the rectangle ABCD intersect at point O ABO is 36 find AOD.

Problems of this type are based on the knowledge that the intersection of diagonals in a rectangle gives us two pairs of identical isosceles triangles. Consider one of such triangles, triangle AOB, in which the angle at the base is known by condition.
Angle ABO = angle BAO = 36 ° (angles at the base of an isosceles triangle).
The angle at the base AOB = 180 ° – (36 ° + 36 °) = 180 ° – 72 ° = 108 °.
The required angle AOD is adjacent to the angle AOB.
Angle AOD = 180 ° – angle AOB = 180 ° – 108 ° = 72 °.
Answer: the AOD angle is 72 °.