# The diagonal of the rectangle makes an angle of 36 degrees with its side.

**The diagonal of the rectangle makes an angle of 36 degrees with its side. Find the value of the angle formed by the diagonals and lying opposite the smaller side of the rectangle.**

Given a rectangle ABCD: AC = BD – diagonals (by the property of rectangle diagonals), ∠OAD = 36 °. The diagonals meet at point O.

The diagonals of the rectangle are halved by the intersection point, then △ AOD is isosceles, since OA = OD. Thus, ∠OAD = ∠ODA = 36 ° (as the angles at the base of an isosceles triangle).

By the sum theorem, the catch of a triangle is:

∠OAD + ∠AOD + ∠ODA = 180 °;

36 ° + ∠AOD + 36 ° = 180 °;

∠AOD = 180 ° – 72 °;

∠AOD = 108 °.

∠AOD and ∠AOB (the angle between the diagonals opposite the smaller side AB) are adjacent angles, then:

∠AOD + ∠AOB = 180 °;

108 ° + ∠AOB = 180 °;

∠AOB = 180 ° – 108 °;

∠AOB = 72 °.

Answer: ∠AOB = 72 °.