In Figure, if PQ\(||\)ST, \(∠\)PQR=110° and \(∠\)RST=130°, find \(∠\)QRS. [Hint: Draw a line parallel to ST through point R.]
Solution and Explanation
Let us draw a line XY parallel to ST and passing through point R.
\(∠\)PQR + \(∠\)QRX = 180º (Co-interior angles on the same side of transversal QR)
\(⇒\) 110º + \(∠\)QRX = 180º
\(⇒\) \(∠\)QRX = 70º
Also,
\(∠\)RST + \(∠\)SRY = 180º (Co-interior angles on the same side of transversal SR)
130º + \(∠\)SRY = 180º
\(∠\)SRY = 50º
XY is a straight line. RQ and RS stand on it.
∴ \(∠\)QRX + \(∠\)QRS +\(∠\)SRY = 180º
70º + \(∠\)QRS + 50º = 180º
\(∠\)QRS = 180º − 120º
= 60º
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