First, note that for angles LMP and NMP you have
[tex]m\angle LMP+m\angle NMP=m\angle NML.[/tex]
If [tex]m\angle LMP[/tex] is [tex]11^{\circ}[/tex] more than [tex]m\angle MNP,[/tex] then
[tex]m\angle LMP=m\angle NMP+11^{\circ}.[/tex]
Now, since [tex]m\angle MNL=137^{\circ},[/tex] you have
[tex]137^{\circ}=m\angle NMP+11^{\circ}+m\angle NMP,\\ \\2m\angle NMP=137^{\circ}-11^{\circ}=126^{\circ},\\ \\m\angle NMP=63^{\circ}.[/tex]
Therefore,
[tex]m\angle LMP=63^{\circ}+11^{\circ}=74^{\circ}.[/tex]
Answer: [tex]m\angle LMP=74^{\circ},\ m\angle NMP=63^{\circ}.[/tex]
