# 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.