Question

In the following figure, if OP || RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to ______.

Options

• 40°

• 50°

• 60°

• 70°

Answer 1

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°