In triangle $ABC$, there is an obtuse angle at vertex $B$, and $AB > BC$. The external angle bisector of angle at $A$ intersects the line $BC$ at point $D$, and the external angle bisector of angle at $B$ intersects the line $AC$ at point $E$. Determine the angles of triangle $ABC$ if $AD = AB = BE$.
The triangles $A B D$ and $A B E$ are isosceles. Using this, we get that the angles of the original triangle are: $\alpha=12^{\circ}, \beta=132^{\circ}, \gamma=36^{\circ}$.