The diagonals of rectangle ABCD meet at point O. The AOB is 80 degrees. Find the CAD and BDC angles.

Rectangle Diagonals Property – The diagonals are equal and are halved at the intersection. Therefore ao = ob, in an isosceles triangle the angles at the base are equal, hence the angle oba = angle oab. According to the theorem about 3 angles of a triangle, their sum = 180 degrees. Therefore, the angle oba = angle oab = (180m-80) / 2 = 50 degrees. The angle oab and the angle cad make up the right angle of the rectangle, hence the angle cad = 90-50 = 40 degrees. The second angle is found from the property of criss-crossing angles. The angle abo and the angle cdo are crosswise at parallel lines ab and cd, by the property of cross-lying angles they are equal. Hence the angle bdc = 50 degrees
Answer: cad = 40, bdc = 50