To solve for [tex]\( x \)[/tex] in the angles [tex]\( (28x - 2)^\circ \)[/tex] and [tex]\( (4x + 19)^\circ \)[/tex], we need to keep in mind that these angles are supplementary, meaning their sum is [tex]\( 180^\circ \)[/tex].
Here are the steps for solving the equation:
1. Set up the equation:
Since the angles are supplementary, their sum is [tex]\( 180^\circ \)[/tex]. Therefore,
[tex]\[
(28x - 2) + (4x + 19) = 180
\][/tex]
2. Combine like terms:
Combine the [tex]\( x \)[/tex] terms and the constants:
[tex]\[
28x - 2 + 4x + 19 = 180
\][/tex]
Simplifies to:
[tex]\[
32x + 17 = 180
\][/tex]
3. Isolate the [tex]\( x \)[/tex] term:
To isolate [tex]\( x \)[/tex], first subtract 17 from both sides of the equation:
[tex]\[
32x + 17 - 17 = 180 - 17
\][/tex]
Simplifies to:
[tex]\[
32x = 163
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by 32 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{163}{32}
\][/tex]
5. Determine the decimal value:
Calculate [tex]\( x \)[/tex]:
[tex]\[
x \approx 5.09375
\][/tex]
So, the value of [tex]\( x \)[/tex] is approximately 5.09375. This doesn't match any of the provided options (A, B, C, or D) in the given list.
None of the choices [tex]\( A. 1, B. 7, C. 12, D. 9 \)[/tex] are correct. However, this detailed solution shows how we arrive at the answer.
