https://file.aiquickdraw.com/mathbot/file/1729549030125iyf864q7.jpg

The image you provided shows two angles formed at a right angle. One angle is labeled \((2a - 1)^\circ\), and the other angle is labeled \((6a - 5)^\circ\). Since these two angles together form a right angle, their sum must be \(90^\circ\).

To solve for \(a\), we can set up the equation:

\[
(2a - 1) + (6a - 5) = 90
\]

Let's solve this step by step:

1. Combine like terms:
   \[
   2a - 1 + 6a - 5 = 90
   \]
   \[
   8a - 6 = 90
   \]

2. Add 6 to both sides to isolate the term with \(a\):
   \[
   8a = 90 + 6
   \]
   \[
   8a = 96
   \]

3. Divide both sides by 8 to solve for \(a\):
   \[
   a = \frac{96}{8} = 12
   \]

So, the value of \(a\) is \(12\).

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:
1. How can we verify that the sum of angles in this problem equals \(90^\circ\)?
2. What are the values of the two angles once \(a\) is found?
3. How would this problem change if the angles did not form a right angle?
4. Can this method be applied to angles that sum to a different value, like \(180^\circ\)?
5. What is the importance of solving for unknowns in geometric problems?

**Tip**: Always remember that angles on a straight line sum to \(180^\circ\) and angles in a right angle sum to \(90^\circ\).

Solve for the value of a using the given angles (2a - 1)° and (6a - 5)° that form a right angle.

Learn how to solve for the value of 'a' by using the sum of angles in a right angle equation. Follow the step-by-step guide to solve (2a - 1)° + (6a - 5)° = 90°. This solution covers algebra and geometry concepts, suitable for students in Grades 7-9.

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