Question

11. In figure, If PQ || ST, ZPQR=110° and ZRST = 120°, then the value of ZQRS is S. *T Q PA 130° 110° R (a) 60° (c) 80° (b) 120° (d) 90°​

Answer 1

Answer:

60°

Step-by-step explanation:

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°