Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $$(M_1)$$ and parallel to the second mirror $$(M_2)$$ is finally reflected from the second mirror $$(M_2)$$ and parallel to the first mirror $$(M_1)$$. The angle between the two mirrors will be:

Let the angle of inclination between the two plane mirrors $$M_1$$ and $$M_2$$ be $$\theta$$.

Ray incident on $$M_1$$ is parallel to $$M_2$$:

$$\text{Glancing angle at } M_1 = \theta \implies \text{Angle of reflection at } M_1 = \theta$$

Ray reflected from $$M_2$$ is parallel to $$M_1$$:

$$\text{Glancing angle at } M_2 = \theta \implies \text{Angle of incidence at } M_2 = \theta$$

In the triangle formed by the two mirrors and the path of the light ray between them:

$$\text{Sum of interior angles} = 180^\circ$$

$$\theta + \theta + \theta = 180^\circ$$

$$3\theta = 180^\circ \implies \theta = 60^\circ$$