Question

Диагонали прямоугольника MNKP пересекаются в точке О, угол MON = 74°. Найдите угол OMP

Answer 1

1) 180-74=106
2) 106/2=53

Answer 2

Finding the Angle OMP

To find the angle OMP, we can use the property that opposite angles in a parallelogram are equal. Since MNKP is a parallelogram, the opposite angles are equal. Therefore, angle MON is equal to angle KMP. Given that angle MON is 74°, we can find angle KMP. Then, we can use the fact that the sum of angles in a triangle is 180° to find angle OMP.

Calculation

- Angle MON = 74° - Since MNKP is a parallelogram, angle MON = angle KMP - Therefore, angle KMP = 74°

Now, to find angle OMP: - The sum of angles in triangle OMP is 180° - We know angle MON = angle KMP = 74° - Therefore, angle OMP = 180° - 74° - 74° - Angle OMP = 32°

So, the measure of angle OMP is 32°.