https://file.aiquickdraw.com/mathbot/file/172558005800682yar11o.jpg

To solve for \( x \) in the given triangle, we can apply the **properties of similar triangles**. The triangle provided seems to represent two triangles that are similar based on corresponding angles being equal (both having the same marked angles).

### Step-by-Step Approach:

1. **Identify the sides of both triangles:**
   - The small triangle has sides: \( 2 \) (height) and \( 3 \) (base).
   - The large triangle has sides: \( x+2 \) (base) and \( 10 \) (hypotenuse).

2. **Set up the ratio for similar triangles:**
   Since the triangles are similar, the ratio of corresponding sides will be equal:
   \[
   \frac{\text{small triangle height}}{\text{large triangle height}} = \frac{\text{small triangle base}}{\text{large triangle base}}
   \]
   This gives:
   \[
   \frac{2}{10} = \frac{3}{x + 2}
   \]

3. **Solve for \( x \):**
   Cross-multiply to solve the proportion:
   \[
   2(x + 2) = 10 \times 3
   \]
   \[
   2(x + 2) = 30
   \]
   \[
   x + 2 = 15
   \]
   \[
   x = 15 - 2
   \]
   \[
   x = 13
   \]

Thus, the value of \( x \) is **13**.

---

Would you like more details or have any questions about this solution?

### Follow-up Questions:
1. How are similar triangles defined, and why can we use them here?
2. What other methods can be used to solve for unknown sides in triangles?
3. Can we apply the Pythagorean theorem in this problem?
4. How do we know the triangles are similar?
5. What would change if one of the angles wasn't marked as equal?

### Tip:
When working with similar triangles, always check for corresponding angles and set up a proportion between corresponding sides.

Solve for x in the given triangle problem where two triangles are similar.

Learn how to solve for x using the properties of similar triangles in a geometric problem. This example demonstrates how to apply the ratio of corresponding sides of similar triangles to find unknown values. Suitable for students in Grades 7-10.

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