Question

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

Explanation:

Step1: Use the property of supplementary angles

When two parallel lines are cut by a transversal, consecutive - interior angles are supplementary. Since \(l\parallel m\), the angle of \(124^{\circ}\) and the angle \((5x - 4)^{\circ}\) are supplementary. So, \(124+(5x - 4)=180\).

Step2: Simplify the equation

First, simplify the left - hand side of the equation: \(124 + 5x-4=180\), which becomes \(5x+120 = 180\).

Step3: Solve for \(x\)

Subtract \(120\) from both sides of the equation: \(5x=180 - 120\), so \(5x=60\). Then divide both sides by \(5\): \(x=\frac{60}{5}\).

Answer:

\(x = 12\)