Question

Кути АОВ і СОВ суміжні, причому кут АОВ=108°. З точки О проведено промінь ОD так, що кут СОD=126°. Чи є промінь OD бісектрисою кута АОВ? Відповідь обґрунтуйте

Answer 1

Ответ:

Луч OD является бисекрисой AB

Answer 2

To determine if the ray OD is the bisector of angle AOV, we need to examine the angles formed by the ray OD and the sides of angle AOV.

Let's break down the given information:

- Angle AOV is 108°. - Angle COD is 126°.

To determine if OD is the bisector of angle AOV, we need to check if angle COD is half of angle AOV.

Calculating the Angle ODC

To find the measure of angle ODC, we subtract the measure of angle COD from 180° (since the sum of the angles in a triangle is 180°).

180° - 126° = 54°

Comparing Angles

Now, let's compare the measure of angle ODC (54°) with the measure of angle AOV (108°).

If angle ODC is half of angle AOV, then ray OD is the bisector of angle AOV.

Conclusion

Since angle ODC (54°) is not half of angle AOV (108°), we can conclude that ray OD is not the bisector of angle AOV.

I hope this explanation helps! Let me know if you have any further questions.