The diagonal rectangles MRKN intersect at point O. The segment OA is the height of the triangle

The diagonal rectangles MRKN intersect at point O. The segment OA is the height of the triangle MOR AOR = 15 degrees. Find the corner ONK.

1. Consider △ OAR: ∠OAR = 90 ° (since OA is the height), ∠AOR = 15 ° (by condition).

By the theorem on the sum of the angles of a triangle: the sum of all interior angles of any triangle is 180 °. Then, for △ OAR:

∠OAR + ∠ARO + ∠AOR = 180 °;

90 ° + ∠ARO + 15 ° = 180 °;

∠ARO = 180 ° – 90 ° – 15 °;

∠ARO = 75 °.

2. In the rectangle MRKH, the pairs of sides MR and KN, MN and RK are parallel (by the definition of a rectangle)

∠ARO = ∠ONK since they are cross-lying angles formed at the intersection of the parallel lines MR and KN of the secant RN.

Thus, ∠ONK = 75 °.

Answer: ∠ONK = 75 °.