Two supplementary angles are in the ratio 2:3. The angles are

Options

A. A)`33^@, 57^@`
B. B)`68^@, 114^@`
C. C)`72^@, 108^@`
D. D)`36^@, 54^@`

Answer

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

### Step-by-Step Solution:

1. **Understanding Supplementary Angles**:
Supplementary angles are two angles whose sum is 180 degrees.

2. **Setting Up the Ratio**:
Let the two angles be represented as \(2k\) and \(3k\), where \(k\) is a common multiplier. This representation maintains the ratio of 2:3.

3. **Writing the Equation**:
Since the angles are supplementary, we can write the equation:
\[ 2k + 3k = 180 \]

4. **Combining Like Terms**:
Combine the terms on the left side of the equation:
\[ 5k = 180 \]

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

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

7. **Conclusion**:
The two supplementary angles are \(72\) degrees and \(108\) degrees.

### Final Answer:
The angles are \(72\) degrees and \(108\) degrees.

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