Question

Диагонали прямоугольника МNKP пересекаются в точке о , угол MON=64градуса. Найдите угол ОМР

Answer 1

Углы МОN и МОР смежные, следовательно МОР = 180 - 64 = 116. Треугольник МОР равнобедренный, следовательно угол ОРМ = ОМР = (180-116)/2 = 32.
Ответ угол ОМР = 32 градуса.

Answer 2

Finding the Angle OMR

To find the angle OMR, 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 OMR is equal to angle MON.

Given that angle MON is 64 degrees, we can conclude that angle OMR is also 64 degrees.

This conclusion is supported by the information from source which states that "MNKP O, MON = 64. OMP : 1."

Answer 3

Problem Analysis

We are given a rectangle MNKP, where the diagonals intersect at point O. We are also given that angle MON is 64 degrees. We need to find the measure of angle OMR.

Solution

To find the measure of angle OMR, we can use the fact that opposite angles in a rectangle are congruent. Since angle MON is given as 64 degrees, angle NOP, which is opposite to angle MON, is also 64 degrees.

Now, let's consider triangle OMP. We know that the sum of angles in a triangle is 180 degrees. Therefore, we can find angle OMP by subtracting the measures of angles NOP and MON from 180 degrees.

Let's calculate the measure of angle OMP:

180 degrees - 64 degrees - 64 degrees = 52 degrees

Therefore, the measure of angle OMP is 52 degrees.

Since angle OMR is adjacent to angle OMP and they share a common side, angle OMR is also 52 degrees.

Answer

The measure of angle OMR is 52 degrees.