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 sum of the angle \((2x + 20)^{\circ}\) and \(54^{\circ}\) is \(180^{\circ}\) (consecutive - interior angles). So, \(2x+20 + 54=180\).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \(2x+(20 + 54)=180\), which gives \(2x+74 = 180\).

Step3: Solve for \(x\)

Subtract \(74\) from both sides: \(2x=180 - 74\), so \(2x=106\). Then divide both sides by \(2\): \(x=\frac{106}{2}\).

Answer:

\(x = 53\)