Mark against the correct answer:
The angles of a triangle are in the ratio 2 : 3:4. The largest angle is

Options

A. `60^(@)`
B. `80^(@)`
C. `76^(@)`
D. `84^(@)`

Answer

To solve the problem of finding the largest angle in a triangle where the angles are in the ratio 2:3:4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio of Angles**:
The angles of the triangle are given in the ratio 2:3:4. This means we can express the angles in terms of a common variable, say \( x \).

2. **Express the Angles**:
- First angle = \( 2x \)
- Second angle = \( 3x \)
- Third angle = \( 4x \)

3. **Use the Triangle Angle Sum Property**:
The sum of all angles in a triangle is always \( 180^\circ \). Therefore, we can write the equation:
\[ 2x + 3x + 4x = 180^\circ \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 9x = 180^\circ \]

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

6. **Find Each Angle**:
Now, substitute \( x \) back into the expressions for each angle:
- First angle = \( 2x = 2 \times 20^\circ = 40^\circ \)
- Second angle = \( 3x = 3 \times 20^\circ = 60^\circ \)
- Third angle = \( 4x = 4 \times 20^\circ = 80^\circ \)

7. **Identify the Largest Angle**:
Among the angles \( 40^\circ, 60^\circ, \) and \( 80^\circ \), the largest angle is \( 80^\circ \).

8. **Select the Correct Option**:
The largest angle is \( 80^\circ \), which corresponds to option 2.

### Final Answer:
The largest angle is \( 80^\circ \) (Option 2).

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