Question

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

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), \(x\) and \(142^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal.
So, \(x = 142\)

Step2: Find the value of \(y\)

\(x\) and \(y\) are supplementary angles (they form a linear pair). The sum of supplementary angles is \(180^{\circ}\).
We know \(x = 142^{\circ}\), then \(y=180 - x\)
Substitute \(x = 142^{\circ}\) into the formula: \(y = 180-142\)
\(y = 38\)

Answer:

\(x = 142\), \(y = 38\)