Question

given ( l parallel m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify angle relationship

Since \( l \parallel m \parallel n \), the angles \( (4x - 8)^\circ \) and \( (6x + 18)^\circ \) are same - side interior angles (or consecutive interior angles) and they are supplementary. So, we can set up the equation:
\( (4x - 8)+(6x + 18)=180 \)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\( 4x-8 + 6x+18=180 \)
\( (4x + 6x)+(-8 + 18)=180 \)
\( 10x+10 = 180 \)

Step3: Solve for x

Subtract 10 from both sides of the equation:
\( 10x+10-10=180 - 10 \)
\( 10x=170 \)
Divide both sides by 10:
\( x=\frac{170}{10}=17 \)

Answer:

\( x = 17 \)