In Figure 5.74 PQ and QR are two mirrors joined at an angle of 30°. The incident ray AB is parallel to the mirror RC then find the values of ∠BCQ, ∠CBQ and ∠BDC.

Let us look at some things that we can derive from the diagram.

After CD there is no reflection. AB is the incident ray.

Now from some properties of reflection, we know that.

Angle of incidence = Angle of Reflection.

If a ray strike at right angle on the mirror, there is no reflection.

Hence, ∠BDC = 90°

And from the figure, ∠ABC = ∠BCQ (Alternate angles of parallel lines AB and CQ)

∠CBD = ∠DQC = 30°

From triangle BCQ, sum of angles of triangle = 180°

30° + ∠BCQ + 30° = 180°

∠BCQ = 180° - 60°

∠BCQ = 120°

And ∠ABC = 120°

So,

∠BCQ = 120°, ∠CBQ = 30°, ∠BDC = 90°