Q19 of 50 Page 6

In Fig., if PQ || ST, ∠ PQR = 110° and∠ RST = 130°, find ∠ QRS.

It is given in the question that:


PQ parallel ST,


∠PQR = 110o and,


∠RST = 130o


Construction: Draw a line XY parallel to PQ and ST



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


110o + ∠QRX = 180o


∠QRX = 70o


And,


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


130o + ∠SRY = 180o


∠SRY = 50o


Now,


∠QRX + ∠SRY + ∠QRS = 180o (Angle made on a straight line)


70o + 50o + ∠QRS = 180o


∠QRS = 60o


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 18

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 20

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 21

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