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+4828x=16x+48

Now, subtract 16x from both sides.

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

28x−16x=16x−16x+48

12x=48

Then, divide both sides by 12.

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

12

12x

=

12

48

x=4

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

Answer 2

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} (12x)/(12)=(48)/(12) \\ x=4 \end{gathered}`

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