The diagonals of the rectangle MNKP intersect at point O, the angle MON is 64 °. Find the angle OMP.

The problem can be solved in different ways.
Option 1.
The intersection of the diagonals gives four isosceles triangles, which are equal in pairs. Consider one of them, the triangle MON, in which the angle at the apex is given and this makes it possible to find the angle at the base.
Angle NMO = (180 ° – 64 °) / 2 = 58 °
Find the OMP angle:
OMP angle = 90 ° – 58 ° = 32 °

Option 2.
Given the condition, the angle OMP is adjacent to the angle MOP, we find this angle:
MOP angle = 180 ° – 64 ° = 116 °.
In turn, the 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 °.
Answer: The OMP angle is 32 °.