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Question
In the following 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°
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Solution
In the following 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°
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