The diagonals of the rectangle МNKP -cross at point O, the angle MON = 64 degrees. Find the OMP angle?

This type of problem allows you to solve them in several ways. Let’s consider two solutions.
The intersection of the diagonals gives four isosceles triangles, which are equal in pairs.
Option 1.
The angle MON given by condition is adjacent to the angle MOP, let us find this angle:
MOP angle = 180 ° – 64 ° = 116 °.
The same angle MOP is the angle at the apex of an isosceles triangle, we can find the angle at the base, the angle OMP:
OMP angle = (180 ° – 116 °) / 2 = 32 °.

Option 2.
Consider one of the obtained isosceles triangles, the triangle MON, in which the angle at the apex is given, we can find the angle at the base.
Angle NMO = (180 ° – 64 °) / 2 = 58 °
Find the OMP angle:
OMP angle = 90 ° – 58 ° = 32 °.
Answer: The OMP angle is 32 °.