Question

Из точки О выходят четыре луча oa OА, ОВ, OC и ОД каждый из углов AОB и CОД является смежным углом ВОС Найдите угол ВОС если угол АОД равен 68 градусам

Answer 1

Так как АОВ и СОД смежные с ВОС, то точки А, О, С - лежат на одной прямой, также как и точки Д, О, В. Из этого исходит, что угол ВОС=АОД=68° - как вертикальные

Answer 2

Problem Analysis

We are given a diagram with point O and four rays emanating from it: OA, OB, OC, and OD. We are told that angles AOD and COD are adjacent angles, and we need to find the measure of angle BOC given that angle AOD is 68 degrees.

Solution

To find the measure of angle BOC, we can use the fact that adjacent angles are supplementary. In other words, the sum of the measures of adjacent angles is 180 degrees.

Since angle AOD is given as 68 degrees, we can find the measure of angle COD by subtracting 68 degrees from 180 degrees:

angle COD = 180 degrees - angle AOD = 180 degrees - 68 degrees = 112 degrees.

Now, we know that angle BOC and angle COD are adjacent angles, so their measures must add up to 180 degrees. Therefore, we can find the measure of angle BOC by subtracting the measure of angle COD from 180 degrees:

angle BOC = 180 degrees - angle COD = 180 degrees - 112 degrees = 68 degrees.

Therefore, the measure of angle BOC is 68 degrees.

Conclusion

In the given diagram, if angle AOD is 68 degrees, then angle BOC is also 68 degrees.