Introduction:
This problem involves the use of two plane mirrors that are inclined to each other at an angle of 120 degrees. A ray of light is incident on either mirror at an angle of 50 degrees. We need to determine the path of the light ray after it reflects off the mirrors.

Analysis:
To solve this problem, we need to use the laws of reflection. According to these laws, the angle of incidence is equal to the angle of reflection, and the incident ray, the reflected ray, and the normal to the mirror all lie in the same plane.

Steps:
The following steps can be followed to solve this problem:

1. Draw a diagram: Draw a diagram of the two mirrors, the incident ray, and the reflected rays. Label the angles of incidence and reflection.

2. Determine the direction of the reflected ray: Use the law of reflection to determine the direction of the reflected ray. The angle of reflection is equal to the angle of incidence, so the reflected ray will make an angle of 50 degrees with the normal to the mirror.

3. Find the angle between the mirrors: Since the mirrors are inclined to each other at an angle of 120 degrees, the angle between them is 60 degrees.

4. Determine the path of the reflected ray: The reflected ray will reflect off the first mirror and then reflect off the second mirror. The angle between the incident ray and the first mirror is 50 degrees, so the angle between the first mirror and the reflected ray is also 50 degrees. The angle between the second mirror and the reflected ray is also 50 degrees. Therefore, the path of the reflected ray will make an angle of 60 degrees with the incident ray.

5. Conclusion: Therefore, the final path of the light ray will make an angle of 60 degrees with the incident ray.

Conclusion:
In conclusion, the path of the light ray after it reflects off the two mirrors is determined by the laws of reflection. By following the above steps, we can determine the final path of the light ray.