Using the diagonals of the rectangle ABCD intersect at point 0, find the angles between

Using the diagonals of the rectangle ABCD intersect at point 0, find the angles between the diagonals if the angle ABO = 30 degrees.

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

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

AC = BD;

AO = OC = BO = OD.

Thus, the triangles formed by the intersection of the diagonals are isosceles.

The angles between the diagonals ∠АОВ = ∠СОD, ∠BOC = ∠АОD.

To calculate the angle ∠AOB, consider the triangle ΔABO. Since the sum of all the angles of the triangle is 180º, and the angle ∠А is equal to the angle ∠В and is 30º, then:

∠AOВ = 180º – ∠AВO – ∠ВAO;

∠АВ = 180º – 30º – 30º = 120º.

∠СОD = ∠АОВ = 120º.

Since the diagonal is an unfolded angle, the value of which is 180º, then:

∠ВOС = 180º – ∠AOВ;

∠ВOС = 180º – 120º = 60º;

∠AOD = ∠BOC = 60º.

Answer: the angles ∠СОD and ∠АОВ are equal to 120º, the angles СОD and ∠BOC are equal to 60º.