\[\boxed{\mathbf{2.}\mathbf{93}}\]
\[\mathbf{Задача\ имеет\ два\ решения.}\]
\[\angle ABC = 80{^\circ};\ \ \angle DBC = 60{^\circ}.\]
\[1)\ \angle ABD = \angle ABC - \angle DBC\]
\[\angle ABD = 80{^\circ} - 60{^\circ} = 20{^\circ}.\]
\[2)\ \angle ABD = \angle ABC + \angle DBC\]
\[\angle ABD = 60{^\circ} + 80{^\circ} = 140{^\circ}.\]