Question

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

Explanation:

Answer:

To solve for \( x \) when \( l \parallel m \parallel n \), we use the property of parallel lines cut by a transversal: consecutive interior angles are supplementary (they add up to \( 180^\circ \)).

The angle of \( 135^\circ \) and \( x^\circ \) are same - side interior angles (or consecutive interior angles) with respect to the transversal cutting the parallel lines \( m \) and \( n \).

So we set up the equation:
\( 135 + x=180 \)

Subtract \( 135 \) from both sides:
\( x = 180 - 135=45 \)

So the value of \( x \) is \( 45 \).