Introduction:
When two plane mirrors are inclined at an angle of 70 degrees, a ray incident on one mirror at an angle θ after reflection falls on the second mirror and is reflected parallel to the first mirror. We need to find the value of θ.

Explanation:
To find the value of θ, we can use the concept of alternate angles and the law of reflection.

Alternate angles:
When two lines are cut by a transversal, alternate angles are formed on opposite sides of the transversal and are congruent. In this case, the incident ray on the first mirror and the reflected ray on the second mirror are alternate angles.

Law of reflection:
The law of reflection states that the angle of incidence is equal to the angle of reflection. This means that the angle at which the incident ray hits the mirror is equal to the angle at which the reflected ray leaves the mirror.

Procedure:
1. Let's assume that the incident ray makes an angle θ with the first mirror.
2. According to the law of reflection, the reflected ray on the first mirror will also make an angle θ with the mirror.
3. Now, this reflected ray falls on the second mirror and gets reflected parallel to the first mirror.
4. Since the two mirrors are inclined at an angle of 70 degrees, the angle between the first mirror and the second mirror is also 70 degrees.
5. Using the concept of alternate angles, the angle at which the reflected ray hits the second mirror is also θ.
6. According to the law of reflection, the angle at which the ray leaves the second mirror is also θ.
7. Since the ray is reflected parallel to the first mirror, the angle between the second mirror and the reflected ray is 70 degrees.
8. Now, we have a triangle formed by the two mirrors and the incident ray. The sum of the angles in a triangle is 180 degrees.
9. Applying this to our triangle, we have:
- Angle between the first mirror and the incident ray = θ
- Angle between the first mirror and the second mirror = 70 degrees
- Angle between the second mirror and the reflected ray = 70 degrees
- Angle between the incident ray and the reflected ray = 180 - (θ + 70 + 70) degrees
10. Since the reflected ray is parallel to the first mirror, the angle between the incident ray and the reflected ray is 0 degrees.
11. Therefore, we have the equation: 180 - (θ + 70 + 70) = 0
12. Solving this equation, we get: θ + 140 = 180
13. Substituting the values, we find: θ = 40 degrees.

Conclusion:
The value of θ is 40 degrees.