Complementary angles are two angles that add up to [tex]\(90^\circ\)[/tex].
Given:
- One angle measures [tex]\(18^\circ\)[/tex]
- The other angle measures [tex]\((8x - 28)^\circ\)[/tex]
To find the value of [tex]\(x\)[/tex], we can set up the equation:
[tex]\[
18^\circ + (8x - 28)^\circ = 90^\circ
\][/tex]
Let's simplify and solve this equation step-by-step.
1. Combine the angles on the left-hand side of the equation:
[tex]\[
18 + 8x - 28 = 90
\][/tex]
2. Simplify the constants on the left-hand side:
[tex]\[
8x - 10 = 90
\][/tex]
3. Add 10 to both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
8x - 10 + 10 = 90 + 10
\][/tex]
[tex]\[
8x = 100
\][/tex]
4. Divide both sides by 8 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{100}{8}
\][/tex]
[tex]\[
x = 12.5
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(12.5\)[/tex]. This matches the first answer choice given:
12.5
20
44.5
16
Thus, the correct answer is:
[tex]\[
\boxed{12.5}
\][/tex]
