# The diagonal of the rectangle forms an angle of 75 ° from one of its sides. Find the angle between the diagonals of this rectangle

May 31, 2020 | Education

| The diagonals of the rectangle are equal and the intersection point is divided in half (by the property of the rectangle).

Consider the triangle ABO (see figure).

AO = BO (as we just found out).

Therefore, the triangle ABO is isosceles.

By the first property of an isosceles triangle:

∠OBA = ∠OAB

By the theorem on the sum of the angles of a triangle:

180 ° = ∠AOB + ∠OBA + ∠OAB

180 ° = ∠AOB + 75 ° + 75 °

∠AOB = 30 °

Answer: 30

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