Question

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

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Here, \(l\parallel m\), and the angle of \(117^{\circ}\) and \(x^{\circ}\) are consecutive interior angles.

Step2: Set up the equation

Since consecutive - interior angles are supplementary, we have the equation \(117 + x=180\).

Step3: Solve for \(x\)

Subtract \(117\) from both sides of the equation: \(x = 180-117\).

Answer:

\(x = 63\)