The bisectors of the angles $A$ and $B$ of the triangle $ABC$ intersect the sides $BC$ and $AC$ at points $D$ and $E$. It is known that $AE + BD = AB$. Find the angle $\angle C$.
Problem
Source: 2005 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p4
Tags: geometry, angles, angle bisector, Ukraine Correspondence