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Leno4ka [110]
2 years 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]2 years 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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<span>7x-6y=14
6x-y=-17
x = -4  y = -7 (SOLUTION) ; in ordered pair form (x,y) = (-4,-7)

</span><span>3x+8y=16
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INFINITE SOLUTIONS: general form = (x,y) = ( x, -(3x/8)+2 )


Edited later:
</span>7x-6y=14
6x-y=-17
From second equation 6x - y = -17, we have y = 6x +17. Substitute this in the first equation to get
7x-6y=14
>> 7x-6(6x+17)=14
>> 7x-36x-102=14
>> 7x-36x=102+14
>> -29x=116
>> x=116/(-29)
>> x=-4

Now plug this value in y = 6x +17, to get
y = 6(-4) + 17 = -24 +17 = -7

So x = -4, y = -7 is the solution.
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