As Given, ∠PQR=∠PRQ
To prove: ∠PQS=∠PRT
According to the question,
∠PQR+∠PQS=180∘ ∣ Linear Pair
⇒∠PQS=180∘−∠PQR--- (i)
Also ∠PRQ+∠PRT=180∘ ∣ Linear Pair
⇒PRT=180∘−∠PRQ
⇒∠PRQ=180∘−∠PQR−−−(ii)(∠PQR=∠PRQ)
From (i) and (ii),
∠PQS=∠PRT=180∘−∠PQR
∴∠PQS=∠PRT [henceproved]