Final answer:
To find the measure of angle NOP, the equation (9x - 19)° = (2x + 5)° + (3x + 16)° is used based on the exterior angle theorem. After solving for x, substitute it back into the expression for m°NOP to obtain 46°.
Step-by-step explanation:
To find the measure of m°NOP, we can use the fact that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Therefore, the measure of angle OPQ (the exterior angle) is equal to the sum of the measures of angles NOP and PNO.
Given that m°OPQ = (9x - 19)°, m°PNO = (2x + 5)°, and m°NOP = (3x + 16)°, the equation to solve is:
(9x - 19)° = (2x + 5)° + (3x + 16)°
We can solve this equation for x and then substitute back to find the measure of m°NOP.
Solving the equation:
Now that we have x, we can find the measure of m°NOP by substituting x into (3x + 16)°:
m°NOP = 3(10) + 16 = 30 + 16 = 46°
Therefore, the measure of angle NOP is 46°.