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The given problem asks to find the value of angle \( x \), given that the ratio of the angles is \( x : y : z = 2 : 3 : 4 \).

### Steps:

1. **Sum of angles in a triangle:**
   The sum of angles in a triangle is always 180°. Therefore, we have:
   \[
   x + y + z = 180^\circ
   \]

2. **Use the ratio to express the angles:**
   Since \( x : y : z = 2 : 3 : 4 \), let the common ratio be \( k \). This means we can express the angles as:
   \[
   x = 2k, \quad y = 3k, \quad z = 4k
   \]

3. **Set up the equation:**
   Substitute the expressions for \( x \), \( y \), and \( z \) into the sum of the angles equation:
   \[
   2k + 3k + 4k = 180^\circ
   \]
   Simplify the equation:
   \[
   9k = 180^\circ
   \]
   Solve for \( k \):
   \[
   k = \frac{180^\circ}{9} = 20^\circ
   \]

4. **Find the value of \( x \):**
   Now, substitute \( k = 20^\circ \) into the expression for \( x \):
   \[
   x = 2k = 2 \times 20^\circ = 40^\circ
   \]

Thus, the value of \( x \) is \( 40^\circ \).

Would you like more details on the steps or help with a different question?

### Additional Related Questions:
1. What is the value of angle \( y \) in this triangle?
2. How would you find the value of angle \( z \) using this method?
3. What is the sum of angles \( y \) and \( z \) together?
4. How does the ratio of angles change if the sum of the angles were different?
5. Can this triangle be classified based on its angles (e.g., acute, right, obtuse)?

### Tip:
When working with angle ratios, always ensure that the sum of angles in any triangle is 180°.

If x : y : z = 2 : 3 : 4, find the value of x.

Learn how to find the value of x when the ratio of angles in a triangle is given as x : y : z = 2 : 3 : 4. The solution includes steps using the triangle angle sum theorem and angle ratios. Suitable for students in Grades 7-9.

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