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Alex_Xolod
2 months ago
6

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

Mathematics
1 answer:
zzz [12.3K]2 months 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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