Final answer:
The measure of angle MNP is 16 degrees, and the measure of angle NMP is 5 degrees.
Step-by-step explanation:
Let's denote the measure of angle MNP as x. According to the given information, angle MNP is 11 degrees more than angle NMP. So, the measure of angle MNP can be represented as x degrees + 11 degrees.
We also know that angle NML is equal to 137 degrees.
Since angles NMP and NML are on the same line, their measures must add up to 180 degrees.
Therefore, we can set up the equation: x + x + 11 + 137 = 180.
Simplifying the equation, we get:
2x + 148 = 180.
Subtracting 148 from both sides, we have:
2x = 32.
Dividing both sides by 2, we get:
x = 16.
Therefore, the measure of angle MNP is 16 degrees, and the measure of angle NMP is 16 degrees - 11 degrees = 5 degrees.