1.

If pq parallel to st and angle q = 105 degree and angle s = 120 find angle qrs​

Answer»

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°


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