Question

in the figure below, l || m. find x.

Explanation:

Step1: Use the property of parallel - lines and angles

When two parallel lines \(l\) and \(m\) are given, we can use the properties of corresponding, alternate, and supplementary angles. Consider the angles formed by the transversals. The sum of the interior angles on the same - side of the transversals and related to the parallel lines \(l\) and \(m\) can be used.
We know that the sum of the angles in a triangle - like formation related to the parallel lines is \(180^{\circ}\).
Let's consider the angle formed by the intersection of the non - parallel lines with the parallel lines.
We have an angle of \(96^{\circ}\) and an angle of \(39^{\circ}\).
The angle adjacent to \(x\) and the sum of \(96^{\circ}\) and \(39^{\circ}\) form a straight - line (a linear pair).
First, find the sum of the two given angles: \(96^{\circ}+39^{\circ}=135^{\circ}\).

Step2: Find the value of \(x\)

Since the sum of the angle adjacent to \(x\) and \(x\) is \(180^{\circ}\) (linear pair), and the angle adjacent to \(x\) is \(135^{\circ}\) (from Step1).
We use the formula \(x = 180^{\circ}-(96^{\circ}+39^{\circ})\).
\(x=180 - 135\).
\(x = 45^{\circ}\)

Answer:

\(x = 45\)