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Question
In the following figure, if OP || RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to ______.
Options
40°
50°
60°
70°
Solution
In the following figure, if OP || RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to 60°.
Explanation:
See the given figure, producing OP, to intersect RQ at X.
Given: OP || RS and RX is a transversal.
So, ∠RXP = ∠XRS ...(Alternative angle)
∠RXP = 130° ...[Given: ∠QRS = 130°]
RQ is a line segment.
So, ∠PXQ + ∠RXV = 180° ...[Linear pair axiom]
∠PXQ = 180° – ∠RXP = 180° – 130°
∠PXQ = 50°
In triangle PQX, ∠OPQ is an exterior angle,
Therefore, ∠OPQ = ∠PXQ + ∠PQX ...[Exterior angle = Sum of two opposite angles]
110° = 50° + ∠PQX
∠PQX = 110° – 50°
∠PQR = 60°
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