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The problem states that \(\angle 1\) and \(\angle 2\) are vertical angles. We know that vertical angles are congruent, meaning their measures are equal.

Given:
- \(\text{m} \angle 1 = (2x + 29)^\circ\)
- \(\text{m} \angle 2 = (3x - 17)^\circ\)

Since \(\angle 1\) and \(\angle 2\) are vertical angles, we can set their measures equal to each other:

\[
2x + 29 = 3x - 17
\]

### Solving for \(x\):
1. Subtract \(2x\) from both sides:
\[
29 = x - 17
\]
2. Add 17 to both sides:
\[
46 = x
\]

Now that we have \(x = 46\), we can substitute this value into the expression for \(\text{m} \angle 2\):

\[
\text{m} \angle 2 = 3x - 17 = 3(46) - 17 = 138 - 17 = 121^\circ
\]

Thus, the measure of \(\angle 2\) is \(121^\circ\).

Would you like any further clarification on the solution?

Here are 5 related questions:
1. What are vertical angles and why are they congruent?
2. How do you solve linear equations with variables on both sides?
3. What happens when supplementary angles are given instead of vertical angles?
4. How can angle relationships help solve geometry problems involving triangles?
5. How would you solve a similar problem if one of the angles were expressed in radians?

**Tip:** Always double-check the algebraic steps to avoid errors when solving for variables in geometry problems.

∠1 and ∠2 are vertical angles. If m∠1 = (2x + 29)° and m∠2 = (3x - 17)°, find the measure of ∠2.

In this problem, we find the measure of ∠2 using vertical angles and algebra. We solve the equation 2x + 29 = 3x - 17 to determine the value of x and substitute it to find the angle. This solution is suitable for students in Grades 7-9 studying algebra and geometry.

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