if PQ parallel to ST, angle PQR=110° and Angle RST=130° find angle QRS
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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°
Hope it's helpful to you
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