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2014 preRMO p16, angle chasing candidate, incenter, incircle related

Source:

August 9, 2019
geometryincenterincircleanglesAngle Chasing

Problem Statement

In a triangle ABCABC, let II denote the incenter. Let the lines AI,BIAI,BI and CICI intersect the incircle at P,QP,Q and RR, respectively. If ∠BAC=40o\angle BAC = 40^o, what is the value of ∠QPR\angle QPR in degrees ?
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