In rhombus ABCD, angle D = 140 degrees. Determine the angles of the triangle AOD

In rhombus ABCD, angle D = 140 degrees. Determine the angles of the triangle AOD (О the point of intersection of the diagonals)

Since the sum of the adjacent angles of the rhombus is 180, the angle BAD + ABC = 180.
Then, the angle ВAD = 180 – 140 = 40.
The opposite angles at the rhombus are equal, then the angle ADС = ABC = 140.
The diagonals of the rhombus intersect at the point of intersection at a right angle, then the angle AOD = 90.
The diagonals of the rhombus divide the corners at the vertices in half.
Angle OAD = ВAD / 2 = 40/2 = 20.
Angle ADO = ADС / 2 = 140/2 = 70.
Answer: The angles of the AOD triangle are 90, 70, 20.