# In rectangle MPKH, diagonal O. Segment OA is the height of triangle MOP, angle AOP = 15 degrees.

In rectangle MPKH, diagonal O. Segment OA is the height of triangle MOP, angle AOP = 15 degrees. What is the OHK angle?

In a rectangle, the diagonals are equal and at the point of intersection they are divided in half, OP = OM = OK = OH. Then the POM triangle is isosceles, and its height is also the bisector of the POM angle, then the POM angle = 2 * AOP = 2 * 15 = 30. The POM angle = MPO as angles at the base of an isosceles triangle. Angle РMO = MPO = (180 – РOM) / 2 = (180 – 30) / 2 = 75.

Triangles POM and KOH are equal on three sides, then the angle HHK = OKН = PMO = MPO = 75.

Answer: The OHK angle is 75.

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