Two complimentary angles differ by `44^@` Find the two angles

Answer

To solve the problem of finding two complementary angles that differ by 44 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Complementary Angles**:
- Complementary angles are two angles whose sum is 90 degrees.
- Let the two angles be \( x \) and \( y \).

2. **Setting Up the Equations**:
- From the problem, we know:
\[ x + y = 90 \quad \text{(1)} \]
- We also know that the angles differ by 44 degrees:
\[ x - y = 44 \quad \text{(2)} \]

3. **Solving the Equations**:
- We can add equations (1) and (2) together:
\[ (x + y) + (x - y) = 90 + 44 \]
- This simplifies to:
\[ 2x = 134 \]

4. **Finding \( x \)**:
- Now, divide both sides by 2:
\[ x = \frac{134}{2} = 67 \]

5. **Finding \( y \)**:
- Substitute \( x \) back into equation (1):
\[ 67 + y = 90 \]
- Solving for \( y \):
\[ y = 90 - 67 = 23 \]

6. **Conclusion**:
- The two angles are:
\[ x = 67^\circ \quad \text{and} \quad y = 23^\circ \]

### Final Answer:
The two complementary angles are \( 67^\circ \) and \( 23^\circ \).

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