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S.OIn Fig. 6.31, if PQ | ST, 2 POR - 110° andZRST = 130°, find ZQRS.[Hint : Draw a line parallel to ST throughpoint R.]RFig. 63​

Answer»

Step-by-step explanation:

Let us draw a parallel line XY to PQ || ST and passing through POINT R.

Sum of interior ANGLE on the same side of the transversal is always = 180°

So that

∠ PQR + ∠ QRX = 180°

Given that ∠ PQR= 110°

110° + ∠QRX = 180°

∠QRX = 180° -110°

∠QRX = 70°

Sum of interior angle on the same side of the transversal is always = 180°

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

Also

130° + ∠SRY = 180°

∠SRY = 50°

XY is a straight line. Use property of linear pair we get

∠QRX + ∠QRS + ∠SRY = 180°

70° + ∠QRS + 50° = 180°

∠QRS = 180° − 120°

= 60°

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