Question

find the value of x.

x =

Explanation:

Step1: Find the measure of $\angle MSQ$

Since $\angle MSQ$ and $163^{\circ}$ are supplementary angles, $\angle MSQ = 180^{\circ}- 163^{\circ}=17^{\circ}$.

Step2: Set up the equation

Because $\angle MSN+\angle NS P+\angle PSQ = 180^{\circ}$ (straight - line angle), we substitute the given angles: $3x+(9x - 5)+17 = 180$.

Step3: Simplify the equation

Combine like terms: $3x+9x-5 + 17=180$, which becomes $12x+12 = 180$.

Step4: Solve for $x$

Subtract 12 from both sides: $12x=180 - 12=168$. Then divide both sides by 12: $x=\frac{168}{12}=14$.

Answer:

$14$