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 non - parallel transversal lines. One angle of the triangle is 101° and another is 50°. Let the third angle of the triangle be y. Then $y+101^{\circ}+50^{\circ}=180^{\circ}$.
So, $y = 180^{\circ}-(101^{\circ}+50^{\circ})=180^{\circ}-151^{\circ}=29^{\circ}$.

Step2: Use the property of alternate interior angles

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

Answer:

$29$