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^ABC+∨PBC=180° (Property of a Line)
On subtracting above equations,
We Know that ∧ABC>∨ACB⇒∧ABC-∨ACB>0
⇒∧QCB-∨PBC>0⇒∧QCB>∨PBC which is same as ∨PBC<∧QCB.

here another thing which proves that PBC is smaller is that QCB is Obtuse and PBC is acute.Diagram makes it clear too.However proof is required as it is asked.
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