Question

Из точки О выходят четыре луча ОА, ОВ, ОС и ОD. Углы СОВ и АОD - вертикальные. Найдите угол АОВ, если угол СОD равен 37°. Сделайте рисунок.( Рисунок можно и не делать) Главное - решение...

Answer 1

Если углы AOD и BOC вертикальны , то и углы DOC и AOB тоже вертикальны. А вертикальные углы равны.
Решение: COD= AOB =37°
Ответ:37°

Answer 2

Problem Analysis

We are given a point O from which four rays OA, OB, OC, and OD originate. We are told that angles COB and AOD are vertical angles, and we need to find the angle AOB given that angle COD is 37°.

Solution

To find the angle AOB, we can use the fact that vertical angles are congruent. This means that angles COB and AOD are equal in measure. Since angle COD is given as 37°, we can conclude that angle COB and angle AOD are both 37°.

Now, to find the angle AOB, we can use the fact that the sum of the angles in a triangle is 180°. Since angle COB and angle AOD are both 37°, the sum of these two angles is 74°. Therefore, angle AOB can be found by subtracting 74° from 180°:

Angle AOB = 180° - 74° = 106°

So, the angle AOB is 106°.

Diagram

Here is a diagram to help visualize the problem:

          O
         /|\
        / | \
       /  |  \
      /   |   \
     /    |    \
    /     |     \
   /      |      \
  /       |       \
 A--------B--------C
          |
          D

In this diagram, point O is the origin of the rays OA, OB, OC, and OD. Angle COB and angle AOD are both 37°, and we need to find the measure of angle AOB.

Conclusion

The angle AOB is 106°.