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

Options

A. `60^(@)`
B. `40^(@)`
C. `80^(@)`
D. `20^(@)`

Explanation

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

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the triangle are given in the ratio 2:4:3. This means we can express the angles in terms of a variable.

2. **Assign Variables**: Let the angles be represented as:
- First angle = \(2x\)
- Second angle = \(4x\)
- Third angle = \(3x\)

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

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

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 the Smallest Angle**: Now that we have the value of \(x\), we can find the smallest angle, which is \(2x\):
\[ 2x = 2 \times 20^\circ = 40^\circ \]

7. **Conclusion**: The smallest angle of the triangle is \(40^\circ\).