Question

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

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, the sum of the interior angles on the same - side of the transversal is \(180^{\circ}\). But here, we can also use the angle - sum property of a triangle. The sum of angles in a triangle is \(180^{\circ}\).
Let's assume the three angles of the triangle are \(55^{\circ}\), \(x^{\circ}\), and \(60^{\circ}\).

Step2: Apply the angle - sum formula

According to the angle - sum formula for a triangle \(A + B + C=180^{\circ}\), where \(A = 55^{\circ}\), \(B=x^{\circ}\), and \(C = 60^{\circ}\).
We have the equation \(55+x + 60=180\).
Simplify the left - hand side: \(x+115 = 180\).
Subtract 115 from both sides: \(x=180 - 115\).

Answer:

\(x = 65\)