For each vertex of triangle $ABC$, the angle between the altitude and the bisectrix from this vertex was found. It occurred that these angle in vertices $A$ and $B$ were equal. Furthermore the angle in vertex $C$ is greater than two remaining angles. Find angle $C$ of the triangle.
Problem
Source: Sharygin 2010 Final 9.1
Tags: geometry, angle bisector, Angle Chasing, angles, altitude