If angles of a triangle are in the ratio `3: 4: 5`, then the angles are:

Options

A. `45^(@), 60^(@), 75^(@)`
B. `40^(@), 55^(@), 85^(@)`
C. `40^(@), 60^(@), 80^(@)`
D. `45^(@), 55^(@), 80^(@)`

Answer

To find the angles of a triangle given that they are in the ratio of 3:4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of a triangle**: The sum of the angles in any triangle is always 180 degrees.

2. **Set up the ratio**: Let the angles of the triangle be represented as \(3x\), \(4x\), and \(5x\), where \(x\) is a common multiplier.

3. **Write the equation for the sum of angles**:
\[ 3x + 4x + 5x = 180 \]

4. **Combine like terms**:
\[ 12x = 180 \]

5. **Solve for \(x\)**:
\[ x = \frac{180}{12} = 15 \]

6. **Calculate each angle**:
- First angle:
\[ 3x = 3 \times 15 = 45 \text{ degrees} \]
- Second angle:
\[ 4x = 4 \times 15 = 60 \text{ degrees} \]
- Third angle:
\[ 5x = 5 \times 15 = 75 \text{ degrees} \]

7. **Final angles**: The angles of the triangle are \(45\) degrees, \(60\) degrees, and \(75\) degrees.

### Conclusion:
The angles of the triangle are **45 degrees, 60 degrees, and 75 degrees**.

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