Diagonals of rectangle ABCD meet at point O angle ABO = 36, find angle AOD.

In triangle AOB, the angle ABO given by the condition is the angle at the base of an isosceles triangle (two pairs of isosceles triangles give the intersection of the diagonals in the rectangle). Let’s find the angle AOB at the vertex of this triangle:
BOA angle = 180 ° – 2 * 36 ° = 180 ° – 72 ° = 108 °.
The found angle BOA and the angle AOD, which must be found according to the condition of the problem, are adjacent angles.
Angle AOD = 180 ° – 108 ° = 72 °.
Answer: The degree measure of the AOD angle is 72 °.