The diagonals of the rectangle ABCD intersect at point O, the angle ABO = 36 degrees. Find the angle AOD.

Since ABCD is a rectangle, the diagonals AC and BD are divided into equal segments in it. This means that triangle AOB is equal to triangle DOC – they are isosceles, triangle BOС is equal to triangle AOD – isosceles (since BO = OS = AO = OD). Since BO = AO and triangle AOB is isosceles, then the angle ABO is equal to the angle AOB equal to 36 ° => find the angle AOB, in the triangle the sum of all angles is 180 ° => angle AOB = 180 ° – (36 ° + 36 °) = 108 °. Angle AOB and angle AOD are adjacent, since they have one side common BD, in total they give 180 °, from here we calculate the angle AOD: angle AOD = 180 ° -AOB angle = 180 ° -108 ° = 72 °.

Answer: angle AOD = 72 °.