In rhombus ABCD, angle B = 140 degrees, point O is the intersection of the diagonals.

In rhombus ABCD, angle B = 140 degrees, point O is the intersection of the diagonals. Determine the angles of the triangle AOD.

In a rhombus, the opposite angles are equal to each other, and the diagonals of the rhombus divide the angle at the apex in half.

Then the angle ADC = ABC = 140, and the angle ADO = ADC / 2 = 140/2 = 70.

The diagonals of the rhombus intersect at right angles, then the triangle AOD is rectangular. The angle DAO of the triangle AOD is equal to: the angle DAO = 180 – AOD – ADO = 180 – 90 – 70 = 20.

Answer: The angles of triangle AOD are equal to 20, 70, 90.