Question

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

Explanation:

Step1: Identify alternate interior angles

Since \( l \parallel m \parallel n \), the \( 65^\circ \) angle and \( x^\circ \) are alternate interior angles, which are supplementary? No, correct: alternate interior angles for parallel lines cut by a transversal are equal? No, wait, \( x \) and \( 65^\circ \) are same-side interior angles? No, let's correct:

Step1: Recognize same-side interior angles

For parallel lines \( m \) and \( n \), \( x^\circ \) and \( 65^\circ \) are same-side interior angles, so they are supplementary.
$x + 65 = 180$

Step2: Solve for \( x \)

Subtract 65 from both sides.
$x = 180 - 65$
$x = 115$

Answer:

$x = 115$