To find the value of \( x \), we need more information about the relationship between ∠A and ∠B. For example, are ∠A and ∠B supplementary, complementary, or do they form some other type of angle pair? 

Here are common cases to consider:

1. **If ∠A and ∠B are supplementary (sum of angles equals 180°):**
   \[
   \angle A + \angle B = 180°
   \]
   This gives us the equation:
   \[
   (6x + 77) + (3x + 107) = 180
   \]
   Simplifying:
   \[
   9x + 184 = 180
   \]
   Subtract 184 from both sides:
   \[
   9x = -4
   \]
   Divide by 9:
   \[
   x = -\frac{4}{9}
   \]

2. **If ∠A and ∠B are complementary (sum of angles equals 90°):**
   \[
   \angle A + \angle B = 90°
   \]
   The equation becomes:
   \[
   (6x + 77) + (3x + 107) = 90
   \]
   Simplifying:
   \[
   9x + 184 = 90
   \]
   Subtract 184 from both sides:
   \[
   9x = -94
   \]
   Divide by 9:
   \[
   x = -\frac{94}{9}
   \]

Could you specify whether ∠A and ∠B are supplementary or complementary?

---

Would you like further clarification on these calculations? Here are five related questions you might explore:

1. What are complementary and supplementary angles?
2. How do you solve for unknowns in geometric angle problems?
3. What if ∠A and ∠B were vertically opposite angles? How would that affect x?
4. How can you check if your solution for x is correct?
5. How do we interpret negative angle values in geometry?

**Tip**: Always verify the relationship between angles (e.g., supplementary, complementary) before solving.

Discover how to solve for x in the angle problem where ∠A = (6x + 77)° and ∠B = (3x + 107)°. Explore solutions for both supplementary and complementary angle cases, using key geometric and algebraic concepts. This step-by-step guide is ideal for Grades 7-9.

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