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# In figure, sides QP and RQ of $$\angle{PQR}$$ are produced to points S and T, respectively. If $$\angle{SPR}$$ = $$135^\circ$$ and $$\angle{PQT}$$ = $$110^\circ$$ , find $$\angle{PRQ}$$.

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.
$$\because$$ $$\angle{RPQ}$$ + $$\angle{PRQ}$$ = $$\angle{PQT}$$
$$\Rightarrow$$$$45^\circ$$ + $$\angle{PRQ}$$ = $$110^\circ$$
$$\Rightarrow$$$$\angle{PRQ}$$ = $$110^\circ$$ - $$45^\circ$$
$$\Rightarrow$$ $$\angle{PRQ}$$ = $$65^\circ$$.