Incenter AngleGeometry 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 \(P\).