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# In figure, if lines PQ and RS interest at point T, such that $$\angle{PRT}$$ = $$40^\circ$$ ,$$\angle{RPT}$$ = $$95^\circ$$ and $$\angle{TSQ}$$ = $$75^\circ$$ , find $$\angle{SQT}$$.

Since, we know, exterior angle is equal to sum of interior opposite angles

Thus, we get,
$$\Rightarrow$$ $$\angle{PTS}$$ = $$\angle{RPT}$$ + $$\angle{PRT}$$
$$\Rightarrow$$ $$\angle{PTS}$$ = $$95^\circ$$ + $$40^\circ$$
$$\Rightarrow$$ $$\angle{PTS}$$ = $$135^\circ$$ .....(given, $$\angle{PRT}$$ = $$40^\circ$$ and $$\angle{RPT}$$ = $$95^\circ$$)

Similarly,

$$\Rightarrow$$ $$\angle{TSQ}$$ + $$\angle{SQT}$$ = $$\angle{PTS}$$
$$\Rightarrow$$ $$75^\circ$$ + $$\angle{SQT}$$ = $$135^\circ$$
$$\Rightarrow$$ $$\angle{SQT}$$ = $$135^\circ$$ - $$75^\circ$$
$$\Rightarrow$$ $$\angle{SQT}$$ = $$60^\circ$$