Question

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

Explanation:

Step1: Use the property of supplementary angles

When two parallel lines \(m\parallel n\) are cut by a transversal, the sum of the interior angles on the same side of the transversal is \(180^{\circ}\). So, \(105^{\circ}+x^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

Subtract \(105^{\circ}\) from both sides of the equation \(105 + x=180\).
\(x = 180 - 105\).

Answer:

\(x = 75\)