In a triangle let and be the intersections of the bisectors of and with the sides respectively. Determine the angles if
%V0
In a triangle $ABC,$ let $D$ and $E$ be the intersections of the bisectors of $\angle ABC$ and $\angle ACB$ with the sides $AC,AB,$ respectively. Determine the angles $\angle A,\angle B, \angle C$ if $\angle BDE = 24 ^{\circ},$ $\angle CED = 18 ^{\circ}.$
Izvor: Međunarodna matematička olimpijada, shortlist 1992
Školjka 
let 
and 
be the intersections of the bisectors of 
and 
with the sides 
respectively. Determine the angles 
if 
