Line from nowhere

Geometry Level 4

Let ABCABC be a right triangle with ABC=90\angle ABC=90^\circ. Let PP be a point on segment ACAC such that APPC=32\frac{AP}{PC}=\frac{3}{2} and let QQ be a point on segment ABAB such that AQ=3QBAQ=3\cdot QB. If AQP=2PQC\angle AQP=2 \angle PQC, what is the measure (in degrees) of PQC\angle PQC ?

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