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Leno4ka [110]
1 year ago
6

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

Mathematics
1 answer:
Agata [3.3K]1 year ago
7 0

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}.


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