# Line from nowhere

Geometry Level 4

Let $$ABC$$ be a right triangle with $$\angle ABC=90^\circ$$. Let $$P$$ be a point on segment $$AC$$ such that $$\frac{AP}{PC}=\frac{3}{2}$$ and let $$Q$$ be a point on segment $$AB$$ such that $$AQ=3\cdot QB$$. If $$\angle AQP=2 \angle PQC$$, what is the measure (in degrees) of $$\angle PQC$$ ?

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