In a triangle $ABC$, let $I$ denote the incenter. The lines $AI$, $BI$, and $CI$ intersect the incircle at points $P$, $Q$, and $R$, respectively. Given that $\angle BAC = 40^\circ$, determine the value of $\angle QPR$ in degrees.

Let's think step by step and output the final answer within \boxed{}.
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