The angles of a triangle are in the ratio of `2:3:4`. Find the

Options

A. `30^(@)`
B. `60^(@)`
C. `100^(@)`
D. `80^(@)`

Answer

To find the angles of a triangle given that they are in the ratio of 2:3:4, we can 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 that if we let the common multiple be \( x \), we can express the angles as:
- First angle = \( 2x \)
- Second angle = \( 3x \)
- Third angle = \( 4x \)

2. **Sum of Angles in a Triangle**: The sum of the angles in any triangle is always \( 180^\circ \). Therefore, we can set up the equation:
\[ 2x + 3x + 4x = 180^\circ \]

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

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

5. **Calculate Each Angle**:
- First angle:
\[ 2x = 2 \times 20^\circ = 40^\circ \]
- Second angle:
\[ 3x = 3 \times 20^\circ = 60^\circ \]
- Third angle:
\[ 4x = 4 \times 20^\circ = 80^\circ \]

6. **Final Angles**: The angles of the triangle are:
- First angle: \( 40^\circ \)
- Second angle: \( 60^\circ \)
- Third angle: \( 80^\circ \)

### Summary of Angles:
The angles of the triangle are \( 40^\circ, 60^\circ, \) and \( 80^\circ \).

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