Question

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

Explanation:

Step1: Use the property of parallel lines and transversals

When two parallel lines \(l\parallel m\) are cut by a transversal, the sum of the interior angles on the same - side of the transversal is \(180^{\circ}\). Also, we know that the sum of angles in a triangle is \(180^{\circ}\). Let's first find the third angle of the triangle.
Let the third angle of the triangle be \(y\). Then \(y + 65^{\circ}+60^{\circ}=180^{\circ}\) (angle - sum property of a triangle).

$$y=180^{\circ}-(65^{\circ} + 60^{\circ})=180^{\circ}-125^{\circ}=55^{\circ}$$

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:

\(55\)