Write the supplement of each of the following angles:
`83^(@) 45'30''`

Answer

To find the supplement of the angle \(83^\circ 45' 30''\), we need to 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 subtract that angle from \(180^\circ\).

### Step 2: Write the angle in a suitable format
The angle given is \(83^\circ 45' 30''\). We will subtract this from \(180^\circ\).

### Step 3: Convert \(180^\circ\) into degrees, minutes, and seconds
We can express \(180^\circ\) as:
\[ 180^\circ = 179^\circ + 59' + 60'' \]
This is useful because it allows us to perform the subtraction more easily.

### Step 4: Set up the subtraction
Now we can set up the subtraction:
\[ \text{Supplement} = 180^\circ - (83^\circ 45' 30'') \]
Substituting the values we have:
\[ \text{Supplement} = (179^\circ 59' 60'') - (83^\circ 45' 30'') \]

### Step 5: Perform the subtraction
Now we will subtract the angles step by step:
1. **Subtract the seconds**:
\[ 60'' - 30'' = 30'' \]
2. **Subtract the minutes**:
\[ 59' - 45' = 14' \]
3. **Subtract the degrees**:
\[ 179^\circ - 83^\circ = 96^\circ \]

### Step 6: Combine the results
Now we combine the results from the subtraction:
\[ \text{Supplement} = 96^\circ 14' 30'' \]

### Final Answer
The supplement of the angle \(83^\circ 45' 30''\) is:
\[ \boxed{96^\circ 14' 30''} \]

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