Question

in the figure below, ( l parallel m ). find ( x ).

Explanation:

Step1: Find the adjacent - angle of \(135^{\circ}\)

The adjacent - angle of \(135^{\circ}\) is \(180^{\circ}-135^{\circ}=45^{\circ}\) (supplementary angles).

Step2: Use the sum of angles in a triangle - like structure (due to parallel lines)

Since \(l\parallel m\), we know that \(x + 50=135\) (alternate interior angles and angle - sum property). Or using the property of angles formed by parallel lines and transversals:
The sum of the three angles (the angle we found \(45^{\circ}\), \(50^{\circ}\) and \(x\)) related to the parallel lines \(l\) and \(m\) gives \(x=135-(180 - 135)-50\).
Another way: Let's use the property of parallel lines. The angle adjacent to \(135^{\circ}\) is \(45^{\circ}\).
We know that \(x+45 + 50=135\) (by the property of angles formed by a transversal with parallel lines, the sum of the non - overlapping angles between the parallel lines).

$$x=135-(45 + 50)$$

$$x=135 - 95$$

Answer:

\(x = 40\)