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).`