https://file.aiquickdraw.com/mathbot/file/172688289093389dlt57t.jpg

The image presents two intersecting lines \(AC\) and \(DB\) at point \(O\), forming vertical angles. We are given:

- \( m \angle 2 = (8x + 7)^\circ \)
- \( m \angle 4 = (9x)^\circ \)

Since \(\angle 2\) and \(\angle 4\) are **vertical angles**, they are congruent. Therefore, we can set the two expressions equal to each other:

\[
8x + 7 = 9x
\]

Let's solve for \(x\):

\[
8x + 7 = 9x
\]
\[
7 = 9x - 8x
\]
\[
7 = x
\]

Now that we have \(x = 7\), substitute this value back into the expression for \( m \angle 2 \):

\[
m \angle 2 = 8x + 7 = 8(7) + 7 = 56 + 7 = 63^\circ
\]

Thus:
- \(x = 7\)
- \(m \angle 2 = 63^\circ\)

Would you like a detailed breakdown of the vertical angle property or have any further questions?

### Related questions:
1. What are complementary and supplementary angles, and how do they differ from vertical angles?
2. How can you verify if two angles are congruent using only their algebraic expressions?
3. What are alternate interior angles, and when do they appear in geometry?
4. How does the property of vertical angles help in solving geometric proofs?
5. What is the angle sum property of a triangle, and how can it be applied in similar problems?

### Tip:
When dealing with intersecting lines, always check for vertical, adjacent, and supplementary angle relationships as they provide quick clues for solving equations.

Find x and the measure of angle 2 in the given diagram where AC intersects DB at point O. The angles m∠2 = (8x + 7)° and m∠4 = (9x)° are vertical angles.

Learn how to solve for x and find the measure of angle 2 using the vertical angle theorem. In this problem, two intersecting lines form congruent vertical angles with algebraic expressions. Suitable for Grades 8-10.

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