lmp=11 more than nmp and nml=137, what are lmp and nmp

Answer 1

Hi Samuel,

If I'm reading your question right, lmp, nmp, and nml are all angles, correct?

In a triangle, the sum of the three angles is 180 degrees. If angle nml is 137, then lmp + nmp = 180 - 137, or 43 degrees.

From the problem, we have that angle lmp is 11 more than angle nmp, so we can write the equation

lmp = 11 + nmp

And because we have lmp + nmp = 43, we can do a substitution.

(11+nmp) + nmp = 43

Now we can combine like terms and solve:

11 + 2(nmp) = 43

2(nmp) = 32

nmp = 16 degrees

If angle nmp is 16 degrees, angle lmp is 43 - 16, which is 27 degrees.

To check ourselves, 16 + 27 + 137 = 180, so our answer checks out.

I hope that helps!

Answer 2

If IM and ML are co-linear, the NMP + IMP = 180 -137 = 43

Let NMP = x

x + x + 11 = 43

x = 16

So NMP = 16, IMP = 27