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Question

If PQ|| ST, PQR=110o and RST=130o, find QRS.
[Hint : Draw a line parallel to ST through point R.]
1484650_74a7dfda2d774f559b9fd57c6aaf8190.PNG

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Solution

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°



1317947_1484650_ans_8b5ba9cd385448b4ba1fbc95df66f50e.PNG

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