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, \(l\parallel m\parallel n\) and the transversal intersects them. The angle of \(117^{\circ}\) and \(x^{\circ}\) are consecutive interior angles.
The formula for supplementary angles is \(a + b=180^{\circ}\). So, \(117 + x=180\).

Step2: Solve for \(x\)

Subtract \(117\) from both sides of the equation \(117 + x=180\).
\(x=180 - 117\).
\(x = 63\).

Answer:

\(63\)