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Given triangle PQR, PR>PQ and PS bisects ∠QPR
In ΔPQR
PR>PQ ....(Given )
∴∠PQR>∠PRQ (Angle opposite side of the longer side is greater)
In ΔPQS and RPS
∠PQR=∠PQS=180−(∠PSQ+∠QPS)
∠PRQ=∠PRS=180−(∠PSR+∠RPS)
Given PS is bisector of ∠QPR
Then ∠QPS=∠PRQ
∠PQR>∠PRQ
∴180−(∠PSQ+∠QPS)>180−(∠PSR+∠RPS) ( ∠QPS=∠PRQ)
⇒∠PSQ>∠PSR
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