Question

find the value of x so that l||m. state the converse used

Explanation:

Step1: Identify angle - relationship

If \(l\parallel m\), then the corresponding angles are equal. Here, the angle of \(53^{\circ}\) and \((2x - 9)^{\circ}\) are corresponding angles. So we set up the equation \(2x-9 = 53\).

Step2: Solve the equation for \(x\)

Add 9 to both sides of the equation: \(2x-9 + 9=53 + 9\), which simplifies to \(2x=62\).

Step3: Isolate \(x\)

Divide both sides of the equation \(2x = 62\) by 2: \(x=\frac{62}{2}=31\).
The converse used is the converse of the corresponding - angles postulate which states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.

Answer:

\(x = 31\), Converse of corresponding - angles postulate.