\[\angle NMK = 42{^\circ};\ \ \angle PMN = 90{^\circ} -\]
\[прямой;\ \]
\[\angle EMK = 180{^\circ} - развернутый.\]
\[\angle PME =\]
\[= \angle EMK - \angle NMK - \angle PMN =\]
\[= 180{^\circ} - 90{^\circ} - 42{^\circ} = 48{^\circ}\]
\[Ответ:\ \angle PME = 48{^\circ}.\]