To solve for the value of \( k \), let's follow a step-by-step process.
1. Understand the Problem:
- You're given two angles: one measures \( 130^\circ \), and the other measures \( (8k + 58)^\circ \).
- These angles are vertical angles. Vertical angles are always equal.
2. Set Up the Equation:
Since the angles are equal, we can set up the equation:
[tex]\[
130 = 8k + 58
\][/tex]
3. Solve for \( k \):
- Subtract 58 from both sides:
[tex]\[
130 - 58 = 8k
\][/tex]
- This simplifies to:
[tex]\[
72 = 8k
\][/tex]
- Divide both sides by 8:
[tex]\[
\frac{72}{8} = k
\][/tex]
- Simplifying that, we get:
[tex]\[
k = 9
\][/tex]
4. Conclusion:
The value of [tex]\( k \)[/tex] is [tex]\(\boxed{9}\)[/tex].
