Write the complement of each of the following angles:
`34^(@)`
`27^@`

Options

A. `85^(@`
`33^@`
B. `45^(@`
`63^@`
C. `55^(@`
`33^@`
D. `55^(@`
`38^@`

Answer

To find the complement of the given angles, we will follow these steps:

### Step-by-Step Solution

1. **Understand the Concept of Complementary Angles**:
- Complementary angles are two angles whose sum is 90 degrees.

2. **Identify the Angles**:
- The angles given are \(34^\circ 27'\) and \(27^\circ\).

3. **Calculate the Complement of \(34^\circ 27'\)**:
- We need to find the complement by subtracting \(34^\circ 27'\) from \(90^\circ\).
- First, we can express \(90^\circ\) as \(89^\circ 60'\) (since \(1^\circ = 60'\)).
- Now perform the subtraction:
\[ 90^\circ - 34^\circ 27' = 89^\circ 60' - 34^\circ 27' \]

4. **Subtract the Minutes**:
- Subtract the minutes:
\[ 60' - 27' = 33' \]

5. **Subtract the Degrees**:
- Subtract the degrees:
\[ 89^\circ - 34^\circ = 55^\circ \]

6. **Combine the Results**:
- Therefore, the complement of \(34^\circ 27'\) is:
\[ 55^\circ 33' \]

7. **Calculate the Complement of \(27^\circ\)**:
- Now, we find the complement of \(27^\circ\):
- Again, subtract from \(90^\circ\):
\[ 90^\circ - 27^\circ = 63^\circ \]
- Since there are no minutes involved, the complement is simply:
\[ 63^\circ \]

### Final Answers:
- The complement of \(34^\circ 27'\) is \(55^\circ 33'\).
- The complement of \(27^\circ\) is \(63^\circ\).