# Angle Trisectors Of A Right Triangle

Geometry Level 5

Triangle $$ABC$$ has angles $$\angle A=3\alpha, \angle B=90^\circ$$ and $$\angle C=3\gamma$$. Let $$P$$ be a point in segment $$BC$$ such that $$\angle PAB=\alpha$$, and $$Q$$ be a point in segment $$BA$$ such that $$\angle QCB=\gamma$$. Let $$R$$ be a point within the triangle such that $$\angle RAC=\alpha$$ and $$\angle RCA=\gamma$$. If $$\angle QRC=142^\circ$$, what is the measure (in degrees) of $$\alpha$$?

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