Question

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

Explanation:

Step1: Use the property of alternate - interior angles

Since \(l\parallel m\), the angle adjacent to \(x\) (let's call it \(y\)) and the \(39^{\circ}\) angle are alternate - interior angles. So \(y = 39^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the triangle have angles \(96^{\circ}\), \(y\), and the angle adjacent to \(x\) (in the triangle). Also, \(x+( \text{angle in the triangle})=180^{\circ}\) (linear pair).
The sum of angles in the triangle: \(\text{angle in the triangle}+96^{\circ}+y = 180^{\circ}\). Substitute \(y = 39^{\circ}\), we get \(\text{angle in the triangle}=180^{\circ}-96^{\circ}-39^{\circ}=45^{\circ}\).
Since \(x + 45^{\circ}=180^{\circ}\) (linear pair), then \(x=180^{\circ}-45^{\circ}\).

Answer:

\(x = 135\)