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 $(8x - 9)^{\circ}$ are corresponding angles. So we set up the equation $8x-9 = 53$.

Step2: Solve the equation for $x$

Add 9 to both sides of the equation: $8x-9 + 9=53 + 9$, which simplifies to $8x=62$. Then divide both sides by 8: $x=\frac{62}{8}=\frac{31}{4}=7.75$.

Step3: State the converse

The converse used is the Corresponding - Angles Converse. If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.

Answer:

$x = 7.75$, Corresponding - Angles Converse