The angles of a triangle are in the ratio `2 : 3 : 4`. The largest angle of the triangle is

Options

A. `120^(@)`
B. `100^(@)`
C. `80^(@)`
D. `60^(@)`

Explanation

To find the largest angle of a triangle whose angles are in the ratio of 2:3:4, follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the triangle are given in the ratio of 2:3:4. This means we can express the angles in terms of a variable \( x \). Let:
- Angle A = \( 2x \)
- Angle B = \( 3x \)
- Angle C = \( 4x \)

2. **Set Up the Equation**: The sum of the angles in any triangle is always 180 degrees. Therefore, we can write the equation:
\[ 2x + 3x + 4x = 180 \]

3. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ (2 + 3 + 4)x = 180 \]
\[ 9x = 180 \]

4. **Solve for \( x \)**: To find the value of \( x \), divide both sides of the equation by 9:
\[ x = \frac{180}{9} = 20 \]

5. **Calculate Each Angle**:
- Angle A = \( 2x = 2 \times 20 = 40 \) degrees
- Angle B = \( 3x = 3 \times 20 = 60 \) degrees
- Angle C = \( 4x = 4 \times 20 = 80 \) degrees

6. **Identify the Largest Angle**: Among the angles calculated, the largest angle is:
\[ 80 \text{ degrees} \]

### Final Answer:
The largest angle of the triangle is **80 degrees**.