Question

what is the value of $x$ that makes $m \parallel n$?

the two angles are __ therefore they are __
alternate exterior
same side interior
corresponding
vertical
congruent
supplementary

Explanation:

Step1: Identify angle relationship

The angles are same-side interior angles, so they are supplementary. Their sum equals $180^\circ$.
$$(7x + 5) + (79 - x) = 180$$

Step2: Simplify the left side

Combine like terms.
$$6x + 84 = 180$$

Step3: Isolate the variable term

Subtract 84 from both sides.
$$6x = 180 - 84$$
$$6x = 96$$

Step4: Solve for x

Divide both sides by 6.
$$x = \frac{96}{6}$$

Answer:

$x = 16$

Additionally, fill in the blanks:
The two angles are $\boldsymbol{\text{same side interior}}$ therefore they are $\boldsymbol{\text{Supplementary}}$