Question

If m< LMP is 11 degrees more than m< NMP and m< NML =137, find each measure

Answer 1

First, note that for angles LMP and NMP you have

$m\angle LMP+m\angle NMP=m\angle NML.$

If $m\angle LMP$ is $11^{\circ}$ more than $m\angle MNP,$ then

$m\angle LMP=m\angle NMP+11^{\circ}.$

Now, since $m\angle MNL=137^{\circ},$ you have

$137^{\circ}=m\angle NMP+11^{\circ}+m\angle NMP,\\ \\2m\angle NMP=137^{\circ}-11^{\circ}=126^{\circ},\\ \\m\angle NMP=63^{\circ}.$

Therefore,

$m\angle LMP=63^{\circ}+11^{\circ}=74^{\circ}.$

Answer: $m\angle LMP=74^{\circ},\ m\angle NMP=63^{\circ}.$