In rhombus ABCD, the O-intersection point of the diagonals at angle A is 140 define the angles AOD.

First, let’s draw a rhombus ABCD.

Let’s draw the diagonals AC and BD, which are the bisectors of the angles.

Since the angle A is equal to 140 °, then the angle ADO = CDO = 140/2 = 70 °.

In a rhombus, the angles at the base are adjacent, that is, the total is 180 °, then the angle is A = 180 – 140 = 40 °.

Angle ОАD = 40/2 = 20о.

Then the angle AOD = 180 – 70 – 20 = 90о.