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The diagram shows two lines that form a \( V \) shape, with one angle labeled \( 67^\circ \) and the other angle labeled \( (6a-1)^\circ \). Since the lines form a straight angle at the point where they meet, the sum of the two angles is \( 180^\circ \). Therefore, you can set up the equation:

\[
67^\circ + (6a-1)^\circ = 180^\circ
\]

Solving for \( a \):

\[
6a - 1 = 180 - 67
\]
\[
6a - 1 = 113
\]
\[
6a = 114
\]
\[
a = 19
\]

So, the value of \( a \) is 19.

Would you like to go over the steps in more detail or have any other questions about this problem?

**Related Questions:**
1. How would the equation change if the angle was labeled as \( (6a+1)^\circ \) instead?
2. What happens if both angles were equal?
3. What would be the value of \( a \) if the known angle was \( 75^\circ \) instead of \( 67^\circ \)?
4. How can you verify if two lines are truly perpendicular?
5. What are some real-life applications of solving for angles in this manner?

**Tip:** Remember, when verifying your answers in geometry, it's useful to consider if they logically fit within the constraints of the diagram and the physical reality it represents.

Solve for the value of a given two angles: one angle is 67° and the other is (6a - 1)°, with both angles forming a linear pair.

This problem involves solving for the variable a in a linear pair of angles, where one angle is 67° and the other is (6a - 1)°. Using algebra and the Linear Pair Theorem, find the value of a. Suitable for students in Grades 6-9.

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