Question

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

Explanation:

Step1: Identify angle - relationship for \(x\)

Since \(m\parallel n\), \(x\) and the \(42^{\circ}\) angle are vertical - angles. Vertical angles are equal.
\(x = 42^{\circ}\)

Step2: Identify angle - relationship for \(y\)

\(y\) and the \(42^{\circ}\) angle are corresponding angles. For parallel lines \(m\) and \(n\), corresponding angles are equal.
\(y = 42^{\circ}\)

Answer:

\(x = 42\)
\(y = 42\)