Question

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

Explanation:

Step1: Find the supplementary angle

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. The angle of \(143^{\circ}\) and the angle adjacent to \(x^{\circ}\) (on the same side of the transversal) are supplementary.
Let the adjacent angle to \(x^{\circ}\) be \(y^{\circ}\), then \(y + 143=180\), so \(y = 180 - 143=37\).

Step2: Use the property of parallel lines

Since \(m\parallel n\) and the transversal cuts them, \(x=y\) (alternate - interior angles are equal).

Answer:

\(x = 37\)