The diagonals of the rectangle ABCD meet at point O, ABO = 36 °. Find AOD.

In accordance with the property of a rectangle, its diagonals are equal and when they intersect, they are divided in half, so the triangle ABO is isosceles (AO = BO). Then the angles at equal sides are also equal: ∠ABO = ∠BAO = 36 °.

The sum of the angles of any triangle is 180 °, so the angle ∠AOB = 180 ° – ∠ABO – ∠BAO = 180 ° – 36 ° – 36 ° = 108 °.

The diagonal BD with the middle at point O forms a developed angle of 180 °: ∠BOD = 180 °. Then ∠AOD = ∠BOD – ∠AOB = 180 ° – 108 ° = 72 °.