In Figure, $∠$ PQR = $∠$ PRQ, then prove that $∠$ PQS = $∠$ PRT.

Question

In Figure,  $∠$ PQR =  $∠$ PRQ, then prove that  $∠$ PQS =  $∠$ PRT.

cdquestions Admin · Accepted Answer

In the given figure, ST is a straight line and ray QP stands on it.

ST is a straight line and ray QP stands on it
∴ $∠$PQS + $∠$PQR = 180º (Linear Pair)
$∠$PQR = 180º − $∠$PQS............ (1)
$∠$PRT + $∠$PRQ = 180º (Linear Pair)
$∠$PRQ = 180º − $∠$PRT............ (2)
It is given that $∠$PQR =$∠$ PRQ.
Equating equations (1) and (2), we obtain
180º − $∠$PQS = 180º− $∠$PRT
$∠$PQS = $∠$PRT

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, \(∠\)PQR = \(∠\)PRQ, then prove that \(∠\)PQS = \(∠\)PRT.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions