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

Question

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

cdquestions Admin · Accepted Answer

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

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

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

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions