Question

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

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, consecutive interior angles are supplementary. That is, the sum of the two angles is \(180^{\circ}\).
Let the angle of \(116^{\circ}\) and \(x^{\circ}\) be consecutive interior angles. So we have the equation \(116 + x=180\).

Step2: Solve the equation for \(x\)

Subtract \(116\) from both sides of the equation \(116 + x=180\).
\(x=180 - 116\)
\(x = 64\)

Answer:

\(64\)