Question

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

Explanation:

Step1: Apply the property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. But here, since \(l\parallel m\parallel n\), we can use the property that alternate interior angles are equal. The angle of \(59^{\circ}\) and \(x^{\circ}\) are supplementary because \(l\parallel n\) and the transversal forms a linear - pair - like relationship (by the transitive property of parallel lines). The sum of supplementary angles is \(180^{\circ}\).
So, we have the equation \(x + 59=180\).

Step2: Solve the equation for \(x\)

Subtract \(59\) from both sides of the equation \(x + 59=180\).
\(x=180 - 59\).

Answer:

\(121\)