Question

given l || m || n, find the value of x.

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Since \( l\parallel m\parallel n\), the angle \(126^{\circ}\) and \((3x + 6)^{\circ}\) are supplementary.
So, \(126+(3x + 6)=180\).

Step2: Solve the equation

Simplify the left - hand side of the equation: \(126+3x + 6=132+3x\).
Then the equation becomes \(132+3x=180\).
Subtract 132 from both sides: \(3x=180 - 132\), so \(3x=48\).
Divide both sides by 3: \(x=\frac{48}{3}=16\).

Answer:

\(x = 16\)