keeping in mind that an angle bisector, cuts an angle into two equal halves.
so SR is bisecting ∡PST, meaning ∡PSR = ∡RST.
and SQ is bisecting ∡RST, meaning ∡RSQ = ∡QST.
what the dickens does all that mean?
[tex]\bf \stackrel{\measuredangle RSQ}{3x+5}~~=~~\stackrel{\measuredangle QST}{5x-11}\implies 16=2x\implies \cfrac{16}{2}=x\implies \boxed{8=x}
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\measuredangle QST=5(8)-11\implies \measuredangle QST=29=\measuredangle RSQ
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[tex]\bf \measuredangle RST=\measuredangle QST+\measuredangle RSQ\implies \measuredangle RST=29+29\implies \measuredangle RST=58
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\measuredangle PST=\stackrel{\measuredangle RST}{58}+\stackrel{\measuredangle PSR}{58}\implies \measuredangle PST=116[/tex]
