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This image shows two intersecting lines that form vertically opposite angles. In this setup, the vertically opposite angles are equal. We have two expressions for these angles:

1. \( (4x + 7)^\circ \)
2. \( (2x + 5)^\circ \)

Since these are vertically opposite angles, we set them equal to each other:

\[
4x + 7 = 2x + 5
\]

### Solving for \( x \):

1. Subtract \( 2x \) from both sides:
   \[
   4x - 2x + 7 = 5
   \]
   \[
   2x + 7 = 5
   \]

2. Subtract 7 from both sides:
   \[
   2x = -2
   \]

3. Divide by 2:
   \[
   x = -1
   \]

### Conclusion:
The solution is \( x = -1 \).

Would you like a more detailed explanation, or do you have any questions?

Here are some additional related questions:
1. What are vertically opposite angles?
2. How can we determine if two angles are supplementary?
3. What happens to angle relationships when parallel lines are intersected by a transversal?
4. How would the solution change if the expressions for the angles were not equal?
5. Can this method be applied if the angle expressions involved multiple variables?

**Tip:** When solving for \( x \) in angle equations, remember to check if the angle measurements make sense (e.g., they should be positive values).

Solve for x given the angles (4x + 7)° and (2x + 5)° are vertically opposite.

Learn how to solve for x in an equation involving vertically opposite angles. This problem covers algebra and the concept of vertically opposite angles, using the equation (4x + 7) = (2x + 5) to find the value of x. Suitable for students in Grades 7-8.

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