# Fishing for Some Angles

Geometry Level 5

Let $$ABC$$ be a triangle with circumcircle $$\omega$$. Let the bisector of $$\angle ABC$$ meet segment $$AC$$ at $$D$$ and circle $$\omega$$ at $$M \neq B$$. The circumcircle of $$\triangle BDC$$ meets line $$AB$$ at $$E \neq B$$, and $$CE$$ meets $$\omega$$ at $$P \neq C$$. The bisector of $$\angle PMC$$ meets segment $$AC$$ at $$Q \neq C.$$ Given that $$PQ = MC,$$ determine the degree measure of $$\angle ABC.$$

$$\textit{Proposed by Ray Li}$$

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