Angle Trisectors Of A Right Triangle

Geometry Level 5

Triangle ABCABC has angles A=3α,B=90 \angle A=3\alpha, \angle B=90^\circ and C=3γ\angle C=3\gamma. Let PP be a point in segment BCBC such that PAB=α\angle PAB=\alpha, and QQ be a point in segment BABA such that QCB=γ\angle QCB=\gamma. Let RR be a point within the triangle such that RAC=α\angle RAC=\alpha and RCA=γ\angle RCA=\gamma. If QRC=142\angle QRC=142^\circ, what is the measure (in degrees) of α\alpha?

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