\[\angle SOE = 51{^\circ};\ \ \angle SOT = 90{^\circ} -\]
\[прямой;\ \ \]
\[\angle MOT = 180{^\circ} - развернутый.\]
\[\angle MOE =\]
\[= \angle MOT - \angle SOT - \angle SOE =\]
\[= 180{^\circ} - 90{^\circ} - 51{^\circ} = 39{^\circ}.\]
\[Ответ:\ \angle MOE = 39{^\circ}.\]