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In the adjacent figure PQ || ST, ∠PQR=110° and ∠RST=130°, find ∠QRS.[Hint : Draw a line parallel to ST through point R.] |
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Answer» Interior angles on the same SIDE of the transversal:The pair of interior angles on the same side of the transversal are called consecutive interior angles or allied angles or co interior angles. If a transversal INTERSECTS two PARALLEL Lines then each pair of interior angles on the same side of the transversal is supplementary. If a transversal intersects two lines such that a pair of alternate interior angles is EQUAL then the two lines are parallel. SOLUTION : 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° HOPE THIS WILL HELP YOU.. |
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