Two complementary angles differ by `8^(@)`. Find the angles.

Answer

To solve the problem of finding two complementary angles that differ by 8 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Complementary Angles**:
Complementary angles are two angles whose sum is 90 degrees.

2. **Assign Variables**:
Let one angle be \( x \). Then, the other angle, being complementary, can be expressed as \( 90 - x \).

3. **Set Up the Equation**:
According to the problem, the two angles differ by 8 degrees. This can be expressed as:
\[ (90 - x) - x = 8 \]

4. **Simplify the Equation**:
Simplifying the left side of the equation gives:
\[ 90 - 2x = 8 \]

5. **Isolate the Variable**:
To isolate \( x \), first subtract 90 from both sides:
\[ -2x = 8 - 90 \]
This simplifies to:
\[ -2x = -82 \]

6. **Solve for \( x \)**:
Divide both sides by -2:
\[ x = \frac{82}{2} = 41 \]

7. **Find the Second Angle**:
Now that we have \( x \), we can find the second angle:
\[ 90 - x = 90 - 41 = 49 \]

8. **Conclusion**:
The two complementary angles are \( 41^\circ \) and \( 49^\circ \).

### Final Answer:
The two angles are \( 41^\circ \) and \( 49^\circ \).