Question

Прямые AB и CD пересекаются в точке О. ОК - биссектриса угла АОD, угол СОК = 118гр. Найдите величину угла BOD

Answer 1

Пусть < СОА = x
Тогда < АОК = 118 -x

< COA + < AOK = 180

x + (118 -x) + (118-x) = 180

x = 56 градусов--- это и есть угол ВОД

Answer 2

Given Information:

We are given that the lines AB and CD intersect at point O. OK is the angle bisector of angle AOD, and angle SOK measures 118 degrees. We need to find the measure of angle BOD.

Solution:

To find the measure of angle BOD, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since angle SOK measures 118 degrees, we can find the measure of angle AOD by subtracting 118 degrees from 180 degrees:

angle AOD = 180 degrees - 118 degrees = 62 degrees.

Since OK is the angle bisector of angle AOD, angle BOK and angle DOK are equal. Therefore, each of these angles measures half of angle AOD:

angle BOK = angle DOK = 62 degrees / 2 = 31 degrees.

Now, we can find the measure of angle BOD by subtracting the sum of angles BOK and DOK from 180 degrees:

angle BOD = 180 degrees - (angle BOK + angle DOK) = 180 degrees - (31 degrees + 31 degrees) = 180 degrees - 62 degrees = 118 degrees.

Therefore, the measure of angle BOD is 118 degrees.

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