Question

In given figure, if OP || RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR = _________.

Answer 1

Extend OP to intersect QR at T.

Now, OU || RS and RT is the transversal.

∴ ∠PTR = ∠SRT (Pair of alternate angles)

⇒ ∠PTR = 130º (∠SRT = 130º)

Now,

∠PTR + ∠PTQ = 180º (Linear pair)

⇒ 130º + ∠PTQ = 180º

⇒ ∠PTQ = 180º − 130º = 50º

In ∆PQT,

∠OPQ = ∠PTQ + ∠PQT (The exterior angle of a triangle is equal to the sum of its opposite interior angles)

⇒ 110º = 50º + ∠PQT

⇒ ∠PQT = 110º − 50º = 60º

Or ∠PQR = 60º

Thus, the measure of ∠PQR is 60º.

In given figure, if OP || RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR = ___60º___.