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, corresponding angles are equal. Here, \( l\parallel m\parallel n\), and the angle of \(63^{\circ}\) and the angle adjacent to \(x^{\circ}\) (on the same side of the transversal) are corresponding angles. Then, using the property that the sum of adjacent angles on a straight line is \(180^{\circ}\).
We have the equation \(x + 63=180\).

Step2: Solve the equation for \(x\)

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

Answer:

\(x = 117\)