Question

in the figure below, $lparallel m$. find $x$.

Explanation:

Step1: Find the third - angle in the triangle

The sum of angles in a triangle is 180°. Let the third - angle in the triangle be $y$. So, $y=180-(55 + 65)$.
$y = 180 - 120=60^{\circ}$

Step2: Use the property of parallel lines

Since $l\parallel m$, the angle $x$ and the third - angle $y$ in the triangle are alternate interior angles. Alternate interior angles formed by two parallel lines and a transversal are equal. So, $x = y$.

Answer:

$x = 60$