\[\angle EMD = 143{^\circ};\ \ \angle AMD =\]
\[= 180{^\circ} - развернутый.\]
\[\angle AME = \angle AMD - \angle EMD =\]
\[= 180{^\circ} - 143{^\circ} = 37{^\circ}.\]
\[Ответ:\ \angle AME = 37{^\circ}.\]