Question

Find the value of x so that l//m. State the converse used

Answer 1

To solve this problem, let's use the alternate interior angles converse to form the following.

The converse we are using allows us to write the following equation.

$28x=16x+48$

Now, subtract 16x from both sides.

$\begin{gathered} 28x-16x=16x-16x+48 \\ 12x=48 \end{gathered}$

Then, divide both sides by 12.

$\begin{gathered} \frac{12x}{12}=\frac{48}{12} \\ x=4 \end{gathered}$

Therefore, the value of x is 4, and the converse used is alternate interior angles.