Question

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

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. The angle adjacent to \(x^{\circ}\) (on the line intersecting \(n\)) and the \(58^{\circ}\) angle (on the line intersecting \(m\)) are vertical - angles.

Step2: Use the property of supplementary angles

Since \(m\parallel n\), the angle adjacent to \(x^{\circ}\) and \(x^{\circ}\) are supplementary (they form a linear pair). Let the angle adjacent to \(x^{\circ}\) be \(y^{\circ}\). We know \(y = 58\) (vertical angles). And \(x + y=180\) (linear - pair of angles). Substitute \(y = 58\) into the equation: \(x+58 = 180\).

Step3: Solve for \(x\)

Subtract 58 from both sides of the equation \(x+58 = 180\). We get \(x=180 - 58\).

Answer:

\(x = 122\)