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In the given figure, if PQ || ST, PQR = 110º and RST = 130º, 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 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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