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

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Let us draw a line XY parallel to ST and passing through point R. ∠PQR + ∠QRX = 180º (Co-interior angles on the same side of transversal QR) ⇒ 110º + ∠QRX = 180º ⇒ ∠QRX = 70º Also, ∠RST + ∠SRY = 180º (Co-interior angles on the same side of transversal...
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Let us draw a line XY parallel to ST and passing through point R.

∠PQR + ∠QRX = 180º (Co-interior angles on the same side of transversal QR)

⇒ 110º + ∠QRX = 180º

⇒ ∠QRX = 70º

Also,

∠RST + ∠SRY = 180º (Co-interior angles on the same side of transversal SR)

130º + ∠SRY = 180º

∠SRY = 50º

XY is a straight line. RQ and RS stand on it.

∴ ∠QRX + ∠QRS + ∠SRY = 180º

70º + ∠QRS + 50º = 180º

∠QRS = 180º − 120º = 60º

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