Question

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

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the alternate interior angles are equal. But here, we can also use the property of consecutive interior angles. The angle of \(134^{\circ}\) and \(x\) are consecutive interior angles. The sum of consecutive interior angles is \(180^{\circ}\).
So, we have the equation \(x + 134^{\circ}=180^{\circ}\)

Step2: Solve the equation for \(x\)

Subtract \(134^{\circ}\) from both sides of the equation:
\(x=180^{\circ}- 134^{\circ}\)
\(x = 46^{\circ}\)

Answer:

\(46\)