Find the supplement of `50^(@)36'52''`.

Explanation

To find the supplement of the angle \(50^\circ 36' 52''\), we will follow these steps:

### Step 1: Understand the concept of supplementary angles
Supplementary angles are two angles whose sum is \(180^\circ\). If we have one angle \(a\), the supplementary angle \(b\) can be found using the equation:
\[ a + b = 180^\circ \]

### Step 2: Write down the given angle
The given angle is:
\[ a = 50^\circ 36' 52'' \]

### Step 3: Convert \(180^\circ\) into degrees, minutes, and seconds
We know that:
- \(1^\circ = 60'\)
- \(1' = 60''\)

To express \(180^\circ\) in degrees, minutes, and seconds:
\[ 180^\circ = 179^\circ + 60' + 60'' = 179^\circ 60' 60'' \]

### Step 4: Set up the equation for the supplementary angle
We can set up the equation:
\[ 50^\circ 36' 52'' + b = 180^\circ \]

### Step 5: Rearrange to find \(b\)
Rearranging gives us:
\[ b = 180^\circ - 50^\circ 36' 52'' \]

### Step 6: Perform the subtraction
Now we will subtract \(50^\circ 36' 52''\) from \(180^\circ\):
1. Start with the degrees:
\[ 180^\circ - 50^\circ = 130^\circ \]
2. Now subtract the minutes:
\[ 60' - 36' = 24' \]
3. Finally, subtract the seconds:
\[ 60'' - 52'' = 8'' \]

### Step 7: Combine the results
Combining the results from the subtraction:
\[ b = 129^\circ 23' 08'' \]

### Final Answer
The supplement of \(50^\circ 36' 52''\) is:
\[ 129^\circ 23' 08'' \]