In the rectangle ABCD O is the intersection point of the diagonals, the angle COD = 50 degrees. Find the angle CBD.

A rectangle is a quadrangle in which opposite sides are equal and all corners are right:

AB = CD;

BC = AD.

The diagonals of the rectangle are equal to each other, and the point of their intersection is halved:

AC = BD;

AO = OC = BO = OD.

Thus, triangles based on the intersection of diagonals are isosceles.

In order to find the degree measure of the angle ∠СВD, consider the triangle ΔВОС. Since this triangle is isosceles, the angles ∠ОВС and ∠ОСВ are equal. To calculate their value, we find the degree measure of the angle ∠BOC.

Since the BOD angle is unfolded, that is equal to 180º, and the value of the ∠СОD angle is 50º, then:

∠VOC = 180º – 50º = 130º.

Since the sum of all the angles of the triangle is 180º, then:

∠ОВС = ∠ОСВ = (180º – 130º) / 2 = 50º / 2 = 25º.

Answer: the angle ∠СВD is equal to 25º.