JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Geometrical Optics

Let the mirrors meet at angle $\theta$. The ray enters parallel to $M_2$, strikes $M_1$, reflects, and must finally leave $M_2$ parallel to $M_1$. Tracing the ray and applying the law of reflection at each mirror, the two mirrors and the ray enclose a triangle whose three angles are each forced to equal $\theta$ by the parallelism conditions. Since the angles of a triangle sum to $180^{\circ }$, $3\theta =180^{\circ }$, so $\theta =60^{\circ }$.