# In the rectangle MPKH, the diagonals intersect at point O. The segment OA is the height of the triangle MOP

In the rectangle MPKH, the diagonals intersect at point O. The segment OA is the height of the triangle MOP, angle A 15. What is the angle OHK?

Since the diagonals of the rectangle are equal and at the point of their intersection they are divided in half, then OP = OM, then the triangle MPA is isosceles.
Then the height OA is also the bisector and median of the triangle. Angle MOA = AOP = 150, then angle MOP = 15 + 15 = 300. Angle KOH = MOP as vertical angles. The HOK triangle is also isosceles, then the OHK angle = (180 – HOK) / 2 = (180 – 30) / 2 = 750.
Answer: The HOK angle is 750.

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