Question

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

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Here, \( l\parallel m\parallel n\), and the angle \(125^{\circ}\) and the angle adjacent to \(x^{\circ}\) (on the same side of the transversal) are supplementary.
Let the adjacent angle of \(x^{\circ}\) be \(y^{\circ}\), then \(y + 125^{\circ}=180^{\circ}\), so \(y = 180^{\circ}- 125^{\circ}=55^{\circ}\).

Step2: Use the property of alternate - interior angles

Since \(l\parallel m\), \(x\) and \(y\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(x=y\).

Answer:

\(x = 55\)