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

Consider a triangle AOB: the diagonals of the rectangle are equal and intersect in the middle, which means OB = OA, triangle AOB is isosceles, the angles at the base are equal.

Angle ABO = angle BAO = 36 °. Find the third corner of the triangle (the sum of the angles of the triangle is 180 °):

Angle AOB = 180 ° – (ABO + BAO) = 180 ° – (36 ° + 36 °) = 180 ° – 72 ° = 108 °.

ВOD angle – expanded angle, equal to 180 °. It consists of two corners AOB and AOD:

ВOD = AOВ + AOD.

AOD angle = 180 ° – 108 ° = 72 °.

Answer: the AOD angle is 72 °.