https://file.aiquickdraw.com/mathbot/file/1726869062480rqr8lky7.jpg

The given image shows two intersecting lines with the angles \( (6s - 7)^\circ \) and \( (5s + 5)^\circ \). These angles are vertical angles, meaning they are equal.

To solve for \( s \), we can set the two expressions equal to each other:

\[
6s - 7 = 5s + 5
\]

### Step-by-step solution:

1. **Move \(5s\) to the left side by subtracting \(5s\) from both sides:**
   \[
   6s - 5s - 7 = 5
   \]
   \[
   s - 7 = 5
   \]

2. **Add 7 to both sides to isolate \(s\):**
   \[
   s = 5 + 7
   \]
   \[
   s = 12
   \]

Thus, the value of \(s\) is **12**.

Would you like more details or have any questions? Here are five related questions:

1. What are vertical angles, and why are they always equal?
2. If the angles were complementary, how would you solve for \(s\)?
3. How would the problem change if the angles were supplementary?
4. What is the sum of the angles around a point where two lines intersect?
5. What would happen if one of the expressions were changed to \(6s + 7\) instead?

**Tip:** Vertical angles are always congruent, making it easy to set their expressions equal to solve for unknown variables.

Solve for the value of s given two vertical angles: (6s - 7)° and (5s + 5)°.

Solve for the value of s by equating vertical angles (6s - 7)° and (5s + 5)°. This problem involves algebraic manipulation and applies the Vertical Angles Theorem. Detailed steps for solving included. Suitable for Grades 8-10.

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