# Find The Angle

Geometry Level 3

In acute $$\triangle ABC,$$ $$\angle BAC = 80^{\circ}.$$ The internal angle bisectors of $$\angle ABC$$ and $$\angle BCA$$ intersect sides $$CA$$ and $$AB$$ at points $$P,Q$$ respectively. Let $$I$$ be the incenter of $$\triangle ABC$$ (the point where $$BP$$ and $$CQ$$ meet). Suppose the circumcenter of $$\triangle PQI$$ lies on the line joining $$A$$ and $$I.$$ Find $$\angle ABI$$ in degrees.

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