Question

find the value of x.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle adjacent to $163^{\circ}$ is $180 - 163=17^{\circ}$. And we know that the sum of the two non - adjacent angles $(3x)^{\circ}$ and $(9x - 5)^{\circ}$ is equal to the vertical angle of the angle adjacent to $163^{\circ}$. So, $3x+(9x - 5)=17$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x+9x-5 = 12x-5$. So the equation becomes $12x-5 = 17$.

Step3: Solve for $x$

Add 5 to both sides of the equation: $12x-5 + 5=17 + 5$, which gives $12x=22$. Then divide both sides by 12: $x=\frac{22}{12}=\frac{11}{6}$.

Answer:

$x = \frac{11}{6}$