The diagonals of the rectangle MNKP intersect at point O, the angle MON is 64 degrees. Find the OMP corner.
| June 9, 2021 | education
MO = OР
The triangle MOР is isosceles.
Angle NOM + angle MOР = 180 degrees – by the sum of adjacent angles.
180 degrees – 64 degrees = 116 degrees.
Angle MOР + angle MOР + angle MOР = 180 degrees – according to the sum of the angles in the triangle.
180 degrees – 116 degrees = 64 degrees (this is the sum of the OMP and OРM angles)
64: 2 = 32 degrees.
Answer: OMP angle = 32 degrees
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