Question

Use the figure below in the given information to determine which value of X would prove m||n.X=

Answer 1

If the lines m and n would be parallel, then the consecutive interior angles must be congruent, i.e. their measures must be the same:

`m<2=m<3`

Next, substitute the given angle measures into the equation:

`2x+15=4x-9`

Solve for x in the equation by first collecting like terms:

`\begin{gathered} 2x-4x=-9-15 \\ -2x=-24 \\ \text{divide both sides of the equation by -2:} \\ (-2x)/(-2)=(-24)/(-2) \end{gathered}`

Next, reduce the fractions to get:

`x=12`