Find the supplement of `81^(@)30'43'`

Answer

To find the supplement of the angle \( 81^\circ 30' 43'' \), we follow these steps:

### Step 1: Understand the concept of supplementary angles
Supplementary angles are two angles whose sum is \( 180^\circ \). Therefore, to find the supplement of a given angle, we can use the formula:
\[ \text{Supplement} = 180^\circ - \text{Given Angle} \]

### Step 2: Write down the given angle
The given angle is:
\[ 81^\circ 30' 43'' \]

### Step 3: Convert \( 180^\circ \) into the same format
We need to express \( 180^\circ \) in degrees, minutes, and seconds:
- \( 180^\circ = 179^\circ 59' 60'' \) (since \( 1^\circ = 60' \) and \( 1' = 60'' \))

### Step 4: Set up the subtraction
Now we set up the subtraction:
\[ \text{Supplement} = 179^\circ 59' 60'' - 81^\circ 30' 43'' \]

### Step 5: Perform the subtraction step by step
1. **Subtract seconds**:
\[ 60'' - 43'' = 17'' \]

2. **Subtract minutes**:
\[ 59' - 30' = 29' \]

3. **Subtract degrees**:
\[ 179^\circ - 81^\circ = 98^\circ \]

### Step 6: Combine the results
Putting it all together, we find:
\[ \text{Supplement} = 98^\circ 29' 17'' \]

### Final Answer
The supplement of \( 81^\circ 30' 43'' \) is:
\[ \boxed{98^\circ 29' 17''} \]