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Answer :
By linear pair axiom,
\(\because \) \(\angle{RPS}\) + \(\angle{RPQ}\) = \(180^\circ\)
\(\Rightarrow \) \(135^\circ\) + \(\angle{RPQ}\) = \(180^\circ\)
\(\Rightarrow \) \(\angle{RPQ}\) = \(180^\circ\) - \(135^\circ\)
\(\Rightarrow \), \(\angle{RPQ}\) = \(45^\circ\)
We also know that, Sum of interior opposite angles is equal to exterior angles.
\(\because \) \(\angle{RPQ}\) + \(\angle{PRQ}\) = \(\angle{PQT}\)
\(\Rightarrow \)\(45^\circ\) + \(\angle{PRQ}\) = \(110^\circ\)
\(\Rightarrow \)\(\angle{PRQ}\) = \(110^\circ\) - \(45^\circ\)
\(\Rightarrow \) \(\angle{PRQ}\) = \(65^\circ\).