https://file.aiquickdraw.com/mathbot/file/1726842869279ggqx7zz5.jpg

The image shows two intersecting lines forming vertical angles. One of the angles is given as \(67^\circ\), and the other angle is expressed as \((6a - 1)^\circ\).

Since these are vertical angles, they are equal. Therefore, we can set up the following equation:

\[
6a - 1 = 67
\]

Let's solve for \(a\):

\[
6a - 1 = 67
\]
\[
6a = 67 + 1
\]
\[
6a = 68
\]
\[
a = \frac{68}{6} = 11.33
\]

Thus, \(a \approx 11.33\).

Would you like further details on how I derived the solution or any clarification? Here are some related questions:

1. What are vertical angles, and why are they equal?
2. How do intersecting lines form angles that are supplementary or congruent?
3. How would you verify this calculation in different geometrical contexts?
4. If a third angle were added, how would that affect the equation setup?
5. How can we generalize this problem to cases with algebraic expressions in geometry?

**Tip:** Vertical angles are always congruent (equal), which is a fundamental property of intersecting lines.

Solve for the value of 'a' in the equation (6a - 1)° = 67° using the property of vertical angles.

In this problem, we solve for 'a' using the property of vertical angles where (6a - 1)° equals 67°. Vertical angles are congruent, meaning they are equal in measure. This problem explores key concepts in algebra and geometry, suitable for students in Grades 8-10.

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