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

Given:
MNCD rectangle,
MK and HP – diagonals,
point O – the point of intersection of the diagonals MK and HP,
angle MON = 64 degrees.
Find the degree measure of the OMP angle -?
Decision:
1. Consider the triangle HOM. It is isosceles in the way that the diagonals of the rectangle are equal to its honey and the intersection point is halved. Therefore, the angle ОНМ = angle ОМН = (180 – 64): 2 = 116: 2 = 58 (degrees).
2. Consider the triangle MPA. He, too, is isosceles. Angle М = 90 degrees, then the angle ОМР = 90 – 58 = 32 (degrees).
Answer: 32 degrees.