Write the complement of each of the following angles:
`42^(@) 36'25''`

Answer

To find the complement of the angle \( 42^\circ 36' 25'' \), we follow these steps:

### Step 1: Understand the concept of complementary angles
Complementary angles are two angles whose sum is \( 90^\circ \). Therefore, to find the complement of a given angle, we subtract it from \( 90^\circ \).

### Step 2: Set up the equation
We need to find the complement of \( 42^\circ 36' 25'' \). This can be expressed as:
\[ \text{Complement} = 90^\circ - 42^\circ 36' 25'' \]

### Step 3: Convert \( 90^\circ \) into a compatible format
To perform the subtraction easily, we can express \( 90^\circ \) as:
\[ 90^\circ = 89^\circ 59' 60'' \]
This is because \( 1 \text{ minute} = 60 \text{ seconds} \), so we can convert \( 90^\circ \) into degrees, minutes, and seconds.

### Step 4: Perform the subtraction
Now we subtract \( 42^\circ 36' 25'' \) from \( 89^\circ 59' 60'' \):
\[ \begin{align*} & \text{Degrees: } 89^\circ - 42^\circ = 47^\circ \\ & \text{Minutes: } 59' - 36' = 23' \\ & \text{Seconds: } 60'' - 25'' = 35'' \end{align*} \]

### Step 5: Combine the results
Putting it all together, we find:
\[ \text{Complement} = 47^\circ 23' 35'' \]

### Final Answer
The complement of \( 42^\circ 36' 25'' \) is \( 47^\circ 23' 35'' \).

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