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15 days ago

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

Mathematics

1 answer:

zzz [4K]15 days ago

7 0

Start by observing that angles LMP and NMP satisfy the following:

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

Given that $m\angle LMP$ exceeds $m\angle MNP,$ by $11^{\circ}$ , then

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

Since $m\angle MNL=137^{\circ},$ , it follows that

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

Consequently,

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

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

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