Question

in the figure below, (lparallel m). find (x).

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let's consider the triangle formed by the transversals and the parallel lines. First, find the third - angle of the triangle formed. Let the third - angle of the triangle be $y$. We know that $y+50^{\circ}+101^{\circ}=180^{\circ}$.
So, $y = 180^{\circ}-(50^{\circ}+101^{\circ})=180^{\circ}-151^{\circ}=29^{\circ}$.

Step2: Use the property of alternate interior angles

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

Answer:

$x = 29$