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4in Fig. 631, ST. TOR 110 andARST-130°. ind. ORS(ht: Draw a line parallel to ST throughpoint)6.31 |
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Answer» Question 4. In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.[Hint : Draw a line parallel to ST through point R.] Solution: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)Also130° + ∠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° plz like my answer ali |
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