In the rectangle MPKH O – the point of intersection of the diagonals PA and HB

In the rectangle MPKH O – the point of intersection of the diagonals PA and HB – the perpendiculars drawn from the vertices P and H to the line MK. It is known that MA = OB. Find the corner of the POM.

Triangles POA and HOB are rectangular, for which the angle POA = HOB as the vertical angles at the intersection of the diagonals, OP = OH as half of the diagonal PH, then the right-angled triangles POA and HOB are equal in hypotenuse and acute angle.

Then OB = OA.

By condition, MA = OB, then MA = OA, which means AR is the median and height of the POM triangle, then the POM triangle is equilateral, and then all its internal angles are 60.

Answer: The POM angle is 60.