In $\triangle \mathrm{MNO}, \mathrm{m} \angle M=(5 x-14)^{\circ}$, $\mathrm{m} \angle N=(4 x+16)^{\circ}$, and $\mathrm{m} \angle O=(4 x-17)^{\circ}$. What is the value of $x$ ?

Step 1 ：Given that in triangle MNO, m∠M = (5x - 14)°, m∠N = (4x + 16)°, and m∠O = (4x - 17)°.

Step 2 ：We know that the sum of the angles in a triangle is always 180 degrees.

Step 3 ：Therefore, we can set up the equation (5x - 14) + (4x + 16) + (4x - 17) = 180.

Step 4 ：Solving this equation gives us the value of x.

Step 5 ：Final Answer: \(\boxed{15}\)