Question

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

Explanation:

Step1: Use the property of parallel lines

When \( l\parallel m\parallel n \), the angles \((9x - 6)^{\circ}\) and \((6x + 6)^{\circ}\) are equal (alternate interior angles for parallel lines \(l\) and \(n\) cut by a transversal). So, \(9x-6=6x + 6\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(9x-6x-6=6x-6x + 6\), which simplifies to \(3x-6 = 6\).
Add \(6\) to both sides: \(3x-6+6=6 + 6\), getting \(3x=12\).
Divide both sides by \(3\): \(x=\frac{12}{3}\).

Answer:

\(x = 4\)