In Fig , if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.[Hint : Draw a line parallel to ST through point R.]
Given :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 = 180° - 110° ∠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° Hence, ∠QRS = 60°
