Question

given (mparallel n), find the value of (x).
(a) what type of angle pair is shown?
alternate interior
alternate exterior
same side interior
same side exterior
corresponding
linear pair
vertical
(b) are the angles congruent or supplementary?
congruent ((angle1=angle2))
supplementary ((angle1 + angle2=180^{circ}))
(c) solve for (x).
check your work: keep trying.
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Explanation:

Step1: Identify angle - pair type

The angles $(8x - 7)^{\circ}$ and $(x + 16)^{\circ}$ are corresponding angles as they are in the same relative position with respect to the parallel lines $m$ and $n$ and the transversal.

Step2: Determine angle - relationship

Corresponding angles formed by parallel lines and a transversal are congruent. So, $8x-7=x + 16$.

Step3: Solve the equation for $x$

Subtract $x$ from both sides:
$8x-x-7=x - x+16$
$7x-7 = 16$
Add 7 to both sides:
$7x-7 + 7=16 + 7$
$7x=23$
Divide both sides by 7:
$x=\frac{23}{7}\approx3.29$

Answer:

a) Corresponding
b) Congruent ($\angle1=\angle2$)
c) $x = \frac{23}{7}$