Question

solve for x.

Explanation:

Step1: Identify angle - relationship

Assume lines $JK$ and $LK$ are parallel, then the angles $(54 - 8x)^{\circ}$ and $(48 - 2x)^{\circ}$ are corresponding angles (or alternate - exterior angles, depending on the parallel - line properties), and they are equal. So we set up the equation $54−8x = 48−2x$.

Step2: Isolate x - terms

Add $8x$ to both sides of the equation:
$54=48 - 2x+8x$.
Simplify the right - hand side: $54 = 48+6x$.

Step3: Solve for x

Subtract 48 from both sides: $54 - 48=6x$.
$6 = 6x$.
Divide both sides by 6: $x = 1$.

Answer:

$1$