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 angle \((9x + 19)^{\circ}\) and \(62^{\circ}\) are supplementary (consecutive - interior angles). So, \((9x+19)+62 = 180\).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \(9x+19 + 62=9x + 81\). Then the equation becomes \(9x+81 = 180\).

Step3: Solve for \(x\)

Subtract 81 from both sides: \(9x=180 - 81\), so \(9x = 99\). Divide both sides by 9: \(x=\frac{99}{9}\).

Answer:

\(x = 11\)