Question

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

Explanation:

Step1: Use the property of parallel - lines and transversals

When two parallel lines \(l\) and \(m\) are cut by a transversal, the sum of the interior angles on the same side of the transversal is \(180^{\circ}\).

Step2: Set up an equation

Let's consider the angles formed by the parallel lines \(l\) and \(m\) and the transversal. We know that \(45^{\circ}+60^{\circ}+x = 180^{\circ}\).

Step3: Solve the equation for \(x\)

First, simplify the left - hand side of the equation: \(45 + 60=105\). So the equation becomes \(105^{\circ}+x = 180^{\circ}\). Then, subtract \(105^{\circ}\) from both sides of the equation: \(x=180^{\circ}-105^{\circ}\).

Answer:

\(x = 75^{\circ}\)