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One angle measures [tex]$130^{\circ}$[/tex], and another angle measures [tex]$(8k + 58)^{\circ}$[/tex]. If the angles are vertical angles, determine the value of [tex]$k$[/tex].

A. [tex]$k = 9$[/tex]
B. [tex]$k = 15$[/tex]
C. [tex]$k = 72$[/tex]
D. [tex]$k = 150$[/tex]

Sagot :

GinnyAnswer
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].
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