It is given in the question that:

∠PQR = ∠PRQ

To prove,

∠PQS = ∠PRT

Now, according to the question (from the figure)

∠PQR + ∠PQS = 180^o (Linear angles pair)

⇒ ∠PQS = 180^o - ∠PQR ...(i)

Similarly,

∠PRQ + ∠PRT = 180^o (Linear angles pair)

⇒ ∠PRT = 180^o - ∠PRQ 

Now, ∠PQR = ∠PRQ (Given)

∠PRQ = 180^o - ∠PQR ..,(ii)

Using (i) and (ii), we get

∠PQS = ∠PRT = 180^o - ∠PQR

Therefore,

∠PQS = ∠PRT

Hence, proved