Question

In Figure, if PQ\(||\)ST, \(∠\)PQR=110° and \(∠\)RST=130°, find \(∠\)QRS. [Hint: Draw a line parallel to ST through point R.]

Answer 1

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