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The problem asks for the degree measure of the largest angle of a triangle where the angles are in the ratio of 2:3:4.

### Step-by-step solution:

1. **Sum of Angles in a Triangle:**
   The sum of the interior angles of any triangle is always \( 180^\circ \).

2. **Set Up the Equation Using the Given Ratio:**
   Let the angles be represented as:
   - \( 2x \), \( 3x \), and \( 4x \)
   where \( x \) is a common factor.

   The sum of these angles must equal \( 180^\circ \). Therefore, the equation is:
   \[
   2x + 3x + 4x = 180^\circ
   \]
   Simplifying:
   \[
   9x = 180^\circ
   \]

3. **Solve for \( x \):**
   \[
   x = \frac{180^\circ}{9} = 20^\circ
   \]

4. **Find the Largest Angle:**
   The largest angle corresponds to \( 4x \):
   \[
   4x = 4 \times 20^\circ = 80^\circ
   \]

Thus, the largest angle is **80 degrees**.

Would you like further details or clarifications? 

### Related Questions:
1. What are the measures of the other two angles in the triangle?
2. How would the solution change if the ratio was different, for example, 1:2:3?
3. Why is the sum of a triangle's interior angles always 180°?
4. Can a triangle have two angles in a 1:1 ratio?
5. How would you calculate the angles if the triangle were not Euclidean, but spherical?

### Tip:
Always remember to check that the sum of the angles in any triangle, regardless of the ratio, must add up to 180°.

The angles of a triangle are in the ratio of 2:3:4. What is the degree measure of the largest angle?

Learn how to find the largest angle in a triangle where the angles are in the ratio of 2:3:4. This problem covers basic geometry and involves using the sum of angles in a triangle to solve for each angle.

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