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 Pend{array}

Question

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 Pend{array}

Accepted Answer

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.

Answer

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.

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

Answer

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