in the figure below, $l \\parallel m$. find $x$.

Explanation:

Step1: Find triangle's third angle

The sum of angles in a triangle is $180^\circ$. Let the third angle be $y$. $y = 180^\circ - 55^\circ - 65^\circ = 60^\circ$

Step2: Find supplementary angle to $y$

Since $l \parallel m$, $x$ and $y$ are same-side interior angles, so they are supplementary. $x = 180^\circ - y = 180^\circ - 60^\circ$

Answer:

$120^\circ$