Question

∠PQR = ∠PRQ, then prove that ∠PQS=∠PRT.In Fig. 6.15.

Answer 1

PRT = PQR + QPR  (EXTERNAL ANGLE IS SUM OF TWO OPPOSITE INTERNAL ANGLES)

PQS = PRQ + QPR  (EXTERNAL ANGLE IS SUM OF TWO OPPOSITE INTERNAL ANGLES)

NOW,

QPR =  PRT - PQR

QPR = PQS - PRQ

NOW EQUATING BOTH WE GET,

PRT - PQR = PQS - PRQ

NOW WE HAVE BEEN GIVEN THAT PQR=PRQ

PRT = PQS  

HENCE PROVED ..

Answer 2

angle PQS=180-anglePQR...(1)

and angle PRT=180-PRQ=180-anglePQR....(2)(because anglePQR=anglePRQ)

from (1)and (2)
we can Wight that PQS=PRT