In the figure, if PQ∥ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.

PQ∥ST, ∠PQR=110° and ∠RST=130°
Construction: A line XY parallel to PQ and ST is drawn.
∠PQR + ∠QRX = 180° (Angles on the same side of transversal)
⇒ 110° + ∠QRX = 180°
⇒ ∠QRX = 70°
Also ∠RST + ∠SRY = 180° (Angles on the same side of transversal)
130° + ∠SRY = 180°
∠SRY = 50°
Now, ∠QRX + ∠SRY + ∠QRS = 180°
⇒ 70° + 50° + ∠QRS = 180°
∴ ∠QRS = 60°