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This problem involves finding the value of \( a \) in a system of vertical angles.

### Key Information:
- The given angles are \( 67^\circ \) and \( (6a - 1)^\circ \).
- Vertical angles are always equal.

### Setup the Equation:
Since the two angles are vertical angles, we can set them equal to each other:
\[
67 = 6a - 1
\]

### Solving for \( a \):

1. Add 1 to both sides of the equation:
\[
67 + 1 = 6a
\]
\[
68 = 6a
\]

2. Divide both sides by 6:
\[
a = \frac{68}{6} = 11.33
\]

Thus, \( a \approx 11.33 \).

Would you like further details or clarifications? Here are five related questions for deeper understanding:

1. What are vertical angles, and why are they equal?
2. How do you identify pairs of vertical angles in different geometrical diagrams?
3. How can you verify your solution for \( a \) by substituting it back into the original equation?
4. Can vertical angles occur in non-crossing lines?
5. How can understanding angle relationships help solve more complex geometry problems?

**Tip:** When working with linear pairs and vertical angles, always keep in mind the property that opposite angles formed by intersecting lines are equal.

Solve for the value of a. Given two vertical angles: 67° and (6a - 1)°.

Learn how to solve for the variable 'a' by applying the Vertical Angles Theorem, where given angles are 67° and (6a - 1)°. Suitable for students in Grades 7-9.

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