To solve for the value of [tex]\( x \)[/tex] given that the angles [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] are supplementary, we start with their definitions:
[tex]\[
\angle A = 4x - 8
\][/tex]
[tex]\[
\angle B = 2x + 2
\][/tex]
Since [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] are supplementary, their sum is [tex]\( 180^\circ \)[/tex]. This gives us the equation:
[tex]\[
(4x - 8) + (2x + 2) = 180
\][/tex]
Next, we simplify the equation by combining like terms:
[tex]\[
4x - 8 + 2x + 2 = 180
\][/tex]
[tex]\[
6x - 6 = 180
\][/tex]
To isolate [tex]\( x \)[/tex], we first add 6 to both sides of the equation:
[tex]\[
6x - 6 + 6 = 180 + 6
\][/tex]
[tex]\[
6x = 186
\][/tex]
Then, we solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[
x = \frac{186}{6}
\][/tex]
[tex]\[
x = 31
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[
\boxed{31}
\][/tex]
So, the best answer is:
A. 31.
