Question

f pq is parallel to st pqr=120 and rst=140 find qrs

Answer 1

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Answer 2

Answer:

Given:

PQ || ST, ∠PQR = 120° and ∠RST = 140°

Construction:

A line XY parallel to PQ and ST is drawn.

∠PQR + ∠QRX = 180° (Angles on the same side of transversal.)

⇒ 120° + ∠QRX = 180°

⇒ ∠QRX = 60°

Also,

∠RST + ∠SRY = 180° (Angles on the same side of transversal.)

⇒ 140° + ∠SRY = 180°

⇒ ∠SRY = 40°

Now,

∠QRX +∠SRY + ∠QRS = 180°

⇒ 60° + 40° + ∠QRS = 180°

⇒ ∠QRS = 80°

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