Question

In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ABC = 46°, then ∠ABP is equal to ______.

Options

• 44°

• 67°

• 13°

• 62°

Answer 1

In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ABC = 46°, then ∠ABP is equal to 67°.

Explanation:

We know that, the angle of incidence is always equal to the angle of reflection.

∠ABP = ∠CBQ

i.e. a = b

Now, sum of all the angles on a straight line is 180°.  .....[∵ ∠ABC = 46°, given]

∴ a + 46° + b = 180°

⇒ 2a = 180° – 46°  .....[∵ a = b]

⇒ 2a = 134°

⇒ a = `134^circ/2` = 67°

∴ ∠ABP = 67°