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 °
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