Two complementary angles are in the ratio `2: 3`, find these angles

Answer

To solve the problem of finding 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**:
Given that the two angles are in the ratio of 2:3, we can represent these angles as:
- First angle = 2x
- Second angle = 3x
Here, 'x' is a common multiplier.

3. **Write the Equation**:
Since the angles are complementary, we can set up the equation:
\[ 2x + 3x = 90 \]

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

5. **Solve for x**:
To find the value of 'x', divide both sides of the equation by 5:
\[ x = \frac{90}{5} = 18 \]

6. **Find Each Angle**:
Now that we have the value of 'x', we can find the two angles:
- First angle = \(2x = 2 \times 18 = 36\) degrees
- Second angle = \(3x = 3 \times 18 = 54\) degrees

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

### Final Answer:
The two complementary angles are **36 degrees** and **54 degrees**.

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