$\begin{array}{l}\text { In } \triangle \mathrm{NOP}, \mathrm{m} \angle N=(9 x+2)^{\circ} \\ \mathrm{m} \angle O=(x+15)^{\circ}, \text { and } \\ \mathrm{m} \angle P=(4 x-5)^{\circ} \text {. Find } \mathrm{m} \angle P\end{array}$

Step 1 ：Translate the problem into a mathematical equation using the fact that the sum of the angles in a triangle is always 180 degrees. The equation is \((9x + 2) + (x + 15) + (4x - 5) = 180\).

Step 2 ：Solve the equation for x. The solution is \(x = 12\).

Step 3 ：Substitute the value of x into the expression for m∠P to find the measure of angle P. The measure of angle P is \(4*12 - 5 = 43\) degrees.

Step 4 ：The final answer is \(\boxed{43}\) degrees.