Question 1191300
Here's how to solve for x and m∠2:

1. **Recognize the relationship between the angles:** ∠2 and ∠3 are vertical angles. Vertical angles are congruent, meaning they have the same measure.

2. **Set up an equation:** Since m∠2 = m∠3, we can write:

   x² - 30 = x³ + 60

3. **Rearrange the equation:** To solve for x, we need to rearrange the equation. However, this equation involves x² and x³, which makes it a cubic equation, and isn't easy to solve directly. The problem likely intended a linear relationship. It is possible there was a typo in the original problem. If we assume that the intended relationship was linear rather than polynomial, and assuming that the intended measures were m∠2 = x - 30 and m∠3 = x + 60, then we can proceed as follows:

   x - 30 = x + 60

4. **Solve for x:**
   Subtract x from both sides:
   -30 = 60  This is not possible.

   It's possible that there was a typo in the original problem.  If the angle measures were instead m∠2 = x - 30 and m∠3 = 2x + 60, then we would proceed as follows:

   x - 30 = 2x + 60
   -90 = x

5. **Substitute x back into the equation for m∠2:**

   m∠2 = x - 30
   m∠2 = -90 - 30
   m∠2 = -120°

Since angle measures can't be negative, it's likely there was a typo in the original problem.  Double-check the given angle measures.  If they were m∠2 = x-30 and m∠3 = x+60, then there is no solution. If they were m∠2 = x-30 and m∠3 = 2x+60, then x = -90 and m∠2 = -120. 

**If you can provide the correct angle measures, I can help you solve the problem accurately.**