https://file.aiquickdraw.com/mathbot/file/1726709799993wmx06dw7.jpg

In this problem, we are asked to identify the angle pair and solve for \( x \).

### Step 1: Identify the Angle Pair
The given angles are positioned such that the two intersecting lines form vertically opposite angles. Vertically opposite angles are always equal. Therefore, we can set the two expressions for the angles equal to each other:
\[
10x + 10 = 11x + 4
\]

### Step 2: Solve for \( x \)
Now, let's solve this equation.

\[
10x + 10 = 11x + 4
\]

Subtract \( 10x \) from both sides:

\[
10 = x + 4
\]

Now, subtract 4 from both sides:

\[
x = 6
\]

### Conclusion
The value of \( x \) is \( 6 \).

Would you like more details on this, or have any other questions?

Here are some related questions to explore:

1. What are vertically opposite angles, and why are they equal?
2. How would you solve this equation if there were more than two intersecting lines?
3. Could supplementary or complementary angles also be used in such diagrams?
4. What are other types of angle pairs found in parallel lines with a transversal?
5. How can this type of equation-solving be applied in geometry problems involving polygons?

**Tip:** Always check for angle relationships (like vertical, corresponding, or alternate interior) in geometric diagrams before solving for unknowns!

Identify the angle pair in the diagram, then solve for x.

In this problem, two angles are given in algebraic expressions and are positioned as vertically opposite angles. Learn how to identify the angle pair and solve for x in the equation 10x + 10 = 11x + 4. Suitable for students in Grades 7-9.

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