Find The Angle

Geometry Level 3

In acute ABC,\triangle ABC, BAC=80.\angle BAC = 80^{\circ}. The internal angle bisectors of ABC\angle ABC and BCA\angle BCA intersect sides CACA and ABAB at points P,QP,Q respectively. Let II be the incenter of ABC\triangle ABC (the point where BPBP and CQCQ meet). Suppose the circumcenter of PQI\triangle PQI lies on the line joining AA and I.I. Find ABI\angle ABI in degrees.

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