If two complementary angles are in the ratio `2:3` then angles will be

Options

A. `25^(@),65^(@)`
B. `108^(@),72^(@)`
C. `36^(@),54^(@)`
D. `40^(@),60^(@)`

Answer

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

### Step-by-Step Solution:

1. **Understand Complementary Angles**:
Complementary angles are two angles whose sum is equal to 90 degrees.

2. **Set Up the Ratio**:
Let the two angles be represented as \(2x\) and \(3x\), where \(x\) is a common multiplier.

3. **Write the Equation**:
Since the sum of the angles is 90 degrees, we can write the equation:
\[ 2x + 3x = 90 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 5x = 90 \]

5. **Solve for \(x\)**:
Divide both sides by 5 to find the value of \(x\):
\[ x = \frac{90}{5} = 18 \]

6. **Find the Angles**:
Now, substitute \(x\) back into the expressions for the angles:
- First angle:
\[ 2x = 2 \times 18 = 36 \text{ degrees} \]
- Second angle:
\[ 3x = 3 \times 18 = 54 \text{ degrees} \]

7. **Conclusion**:
The two complementary angles are \(36\) degrees and \(54\) degrees.

### Final Answer:
The angles are \(36\) degrees and \(54\) degrees.

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