Question

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

Explanation:

Step1: Use alternate - interior angles

Since \(l\parallel m\), the angle alternate - interior to the \(39^{\circ}\) angle within the triangle is also \(39^{\circ}\).

Step2: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the third - angle of the triangle be \(y\). Then \(y + 39^{\circ}+93^{\circ}=180^{\circ}\). So, \(y=180^{\circ}-(39^{\circ} + 93^{\circ})=180^{\circ}-132^{\circ}=48^{\circ}\).

Step3: Use linear - pair property

The angle \(x\) and \(y\) form a linear pair. Since the sum of angles in a linear pair is \(180^{\circ}\), and \(y = 48^{\circ}\), then \(x=180^{\circ}-48^{\circ}=132^{\circ}\).

Answer:

\(132\)