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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