https://file.aiquickdraw.com/mathbot/file/17256758484136uzufi2x.jpg

In the diagram you provided, we are tasked with finding the value of \( s \). The angles given are:

- \( (8s)^\circ \)
- \( (6s - 8)^\circ \)
- A right angle (\( 90^\circ \)) formed by the perpendicular lines.

### Key Observations:

1. The angle \( (8s)^\circ \) and the right angle are adjacent angles on a straight line, meaning they are supplementary and their sum equals \( 180^\circ \). This gives us the equation:
   \[
   8s + 90 = 180
   \]

2. The angles \( (6s - 8)^\circ \), \( 90^\circ \), and \( 8s^\circ \) form angles around a point, adding up to \( 360^\circ \).

### Solving the equation:

#### Step 1: Solve for \( s \) from the supplementary angles

\[
8s + 90 = 180
\]
Subtract 90 from both sides:
\[
8s = 90
\]
Divide both sides by 8:
\[
s = \frac{90}{8} = 11.25
\]

Thus, \( s = 11.25 \).

### Would you like more details or have any questions about this solution?

Here are some related questions you can explore:

1. How do you prove that adjacent angles on a straight line are supplementary?
2. How would the solution change if the angles were not adjacent to a right angle?
3. Can you generalize the method to solve for \( s \) if the angle expressions were different?
4. What are alternate angle theorems, and how do they apply in this problem?
5. How can you verify the value of \( s \) by checking other angle relationships?

**Tip:** Always remember that angles on a straight line sum up to \( 180^\circ \). This property is very useful in solving many geometry problems.

Solve for the value of s in the geometric diagram with the angles (8s)°, (6s - 8)°, and a right angle.

Find the value of s in a geometric problem involving the angles (8s)°, (6s - 8)°, and a right angle. Learn key concepts such as the supplementary angles theorem and how angles around a point sum to 360°.

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