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