two supplementary angles are in the ratio `3:2`, find the angles.

Options

A. `108^@ , 72^@`
B. `118^@ , 72^@`
C. `72^@ , 208^@`
D. None of these

Explanation

To find the two supplementary angles that are in the ratio of 3:2, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the concept of supplementary angles**:
Supplementary angles are two angles whose sum is 180 degrees.

2. **Set up the ratio**:
Let the two angles be represented as \(3x\) and \(2x\), where \(x\) is a common factor.

3. **Write the equation for supplementary angles**:
Since the angles are supplementary, we can write the equation:
\[ 3x + 2x = 180 \]

4. **Combine like terms**:
Combine the terms on the left side of the equation:
\[ 5x = 180 \]

5. **Solve for \(x\)**:
Divide both sides by 5 to find the value of \(x\):
\[ x = \frac{180}{5} = 36 \]

6. **Find the angles**:
Now substitute \(x\) back into the expressions for the angles:
- First angle:
\[ 3x = 3 \times 36 = 108 \text{ degrees} \]
- Second angle:
\[ 2x = 2 \times 36 = 72 \text{ degrees} \]

7. **State the final answer**:
The two supplementary angles are:
- \(108\) degrees
- \(72\) degrees