To solve for the value of [tex]\( x \)[/tex], given that [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] are supplementary and their expressions in terms of [tex]\( x \)[/tex] are [tex]\(\angle A = 4x - 8\)[/tex] and [tex]\(\angle B = 2x + 2\)[/tex], we need to follow these steps:
1. Understand the property of supplementary angles: Supplementary angles are two angles whose measures add up to 180 degrees. Therefore:
[tex]\[
\angle A + \angle B = 180^\circ
\][/tex]
2. Substitute the given expressions for [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex]:
[tex]\[
(4x - 8) + (2x + 2) = 180
\][/tex]
3. Combine like terms:
[tex]\[
4x - 8 + 2x + 2 = 180
\][/tex]
[tex]\[
6x - 6 = 180
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
6x - 6 = 180
\][/tex]
[tex]\[
6x = 180 + 6
\][/tex]
[tex]\[
6x = 186
\][/tex]
[tex]\[
x = \frac{186}{6}
\][/tex]
[tex]\[
x = 31
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 31. The best answer is:
D. 31
