Answer: The measure of angle MNP is 59 degrees.
Explanation:
From the question, it seems like M, N, and O are points on a line, and P is a point not on that line. This forms two adjacent angles MNO and PNO that add up to a straight angle (180°).
The measure of angle MNO is given as 114° and the measure of angle PNO is given as 55°.
So, the measure of angle MNP, which is the difference of angles MNO and PNO (since PNO is part of MNO), can be found by subtracting the measure of angle PNO from the measure of angle MNO:
m/MNP = m/MNO - m/PNO
m/MNP = 114° - 55°
m/MNP = 59°
So, the measure of angle MNP is 59 degrees.