Question

given ( mparallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of adjacent angles

The angle adjacent to \(138^{\circ}\) is \(180 - 138=42^{\circ}\) (since adjacent angles on a straight line sum to \(180^{\circ}\)).

Step2: Use the property of alternate - interior angles

Because \(m\parallel n\), the angle \(x\) and the angle calculated in Step1 are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(x = 42\).

Answer:

\(42\)