Question

ln fig. 6.15, angle pqr equal to angle prq then prove that angle pqs equals to angle prt

Answer 1

ang.PQR = ang.PRQ........1
ang.PQS + ang.PQR = 180
ang.PQS = 180 - ang.PQR. ..........2
ang.PRQ + ang.PRT = 180
ang.PRQ = 180 - ang.PRT. .............3

comparing eqn. 2 and 3
ang.PQS = ang.PRT (by 1) pd

Answer 2

Solutions:

Since rays QP and RP stand on ST.

Hence, ∠SQP + ∠PQR = 180° and ∠SRP + ∠PRT = 180°

=> ∠PQS + ∠PQR = 180° and ∠PRQ + ∠PRT = 180°

=> ∠PQS + ∠PQR = ∠PRQ + ∠PRT

=> ∠PQS + ∠PQR = ∠PQR + ∠PRT ________[Since, ∠PRQ = ∠PQR (Given)]

=> ∠PQS = ∠PRT

( Refer to the attachment )