In rectangle ABCD O is the intersection of the diagonals, angle AOB = 36 degrees. Find Angle BDC and Angle CAD.

Angle COD = AOB as vertical angles. COD = 360.

In the rectangle, the diagonals at the intersection point are divided in half, then OS = OD, and the triangle COD are isosceles, and its angles at the base of the CD are equal. Then ОDС = (180 – 36) / 2 = 72.

Angle ВDC = ОDC = 72.

The angle BOD is expanded and is equal to 180, then the angle AOD = 180 – 36 = 144. The triangle AOD is isosceles, since the sides OA and OD are half of the diagonals of the rectangle, then the angle OAD = ODA = CAD = (180 – 144) / 2 = 18.

Answer: BDC = 72, CAD = 18.




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