# Incenter Angle

Geometry Level 3

In triangle $$ABC$$, points $$D, E, F$$ are on sides $$BC, CA, AB$$ respectively such that $$AD, BE, CF$$ are angle bisectors of triangle $$ABC$$. The lines $$AD, BE, CF$$ are concurrent at $$I$$, the incenter of triangle $$ABC$$. If $$\angle BAC = 92 ^\circ$$, what is the measure (in degrees) of $$\angle EIF$$?

Details and assumptions

The angle bisectors of a triangle refer to the internal angle bisectors of the triangle.

3 lines are concurrent at a point $$P$$ if they intersect at the point $$P$$.

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