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

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:
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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