Assume that the measure of angle NMP is y degrees.
Now we have two givens that we can use to generate two equations:
We know that measure angle LMP is 11 degrees more than NMP. This means that:
measure angle LMP = y + 11 ..............> equation 1
We also know that measure angle LMP added to measure angle NMP will give us measure angle NML (137 degrees).
angle LMP + angle NMP = angle NML ............> equation 2
Substituting with equation 1 in 2:
y + 11 + y = 137
2y + 11 = 137
2y = 137 - 11 = 126
y = 63 degrees
Based on these calculations:
measure angle NMP = 63 degrees
measure angle LMP = 63 + 11 = 74 degrees
