Question

Угол АОВ в 2 раза больше угла ВОС. ОК - биссектриса угла ВОС , ОМ- биссектриса угла АОВ . Найди угол МОК . РЕШИТЕ СРОЧНО ПРОШУ ВАС !!!

Answer 1

Из произвольной точки О проведем лучи ОА и ОВ и ОС. Варианты расположения различные, поэтому разберем их все!
1. ОА в стороне от ОВ.
Если ВОС обозначить х, то МОС=2х, КОС=0,5х и МОК=1,5х, то есть полтора угла ВОС.
2. ОА в Стороне от ОС.
ОС - биссектриса АОВ. Тогда МОК=0,5 х, то есть половина ВОС.
Задача может быть решена только в общем виде.

Answer 2

Problem Analysis

We are given that the angle AOV is twice the size of the angle VOS. We are also told that OK is the bisector of angle VOS and OM is the bisector of angle AOV. We need to find the measure of angle MOK.

Solution

Let's assume the measure of angle VOS is x degrees. Since angle AOV is twice the size of angle VOS, angle AOV will be 2x degrees.

Since OK is the bisector of angle VOS, it divides the angle into two equal parts. So, angle MOK will be x/2 degrees.

Similarly, since OM is the bisector of angle AOV, it divides the angle into two equal parts. So, angle MOA will also be x/2 degrees.

Now, let's consider triangle MOK. The sum of the angles in a triangle is always 180 degrees. So, we can write the equation:

angle MOK + angle MOA + angle AOK = 180 degrees

Substituting the values we know:

x/2 + x/2 + 2x = 180

Simplifying the equation:

2x + 2x + 4x = 360

8x = 360

x = 360/8

x = 45

Therefore, the measure of angle MOK is 45/2 = 22.5 degrees.

Answer

The measure of angle MOK is 22.5 degrees.