Question

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

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), alternate interior angles are equal. But here, \(x\) and \(106^{\circ}\) are consecutive interior angles. The sum of consecutive interior angles is \(180^{\circ}\).
So, \(x + 106^{\circ}=180^{\circ}\)

Step2: Solve for \(x\)

Subtract \(106^{\circ}\) from both sides of the equation:
\(x=180^{\circ}- 106^{\circ}\)
\(x = 74^{\circ}\)

Answer:

\(74\)