The supplement of `123^(@)45'` is :

Options

A. `56^(@)55'`
B. `56^(@)15'`
C. `55^(@)56'`
D. none of these

Answer

To find the supplement of the angle \( 123^\circ 45' \), we will follow these steps:

### Step 1: Understand the concept of supplement
The supplement of an angle is the angle that, when added to the original angle, equals \( 180^\circ \).

### Step 2: Set up the equation
Let the supplement be \( x \). According to the definition of supplementary angles:
\[ x + 123^\circ 45' = 180^\circ \]

### Step 3: Rearrange the equation to solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = 180^\circ - 123^\circ 45' \]

### Step 4: Convert \( 180^\circ \) into degrees and minutes
Since \( 180^\circ \) can be expressed in degrees and minutes, we write:
\[ 180^\circ = 179^\circ 60' \]

### Step 5: Perform the subtraction
Now we subtract \( 123^\circ 45' \) from \( 179^\circ 60' \):
\[ x = (179^\circ 60') - (123^\circ 45') \]

### Step 6: Subtract the degrees and minutes separately
1. Subtract the degrees:
\[ 179^\circ - 123^\circ = 56^\circ \]
2. Subtract the minutes:
\[ 60' - 45' = 15' \]

### Step 7: Combine the results
Now combine the results from the degree and minute subtraction:
\[ x = 56^\circ 15' \]

### Final Answer
The supplement of \( 123^\circ 45' \) is:
\[ \boxed{56^\circ 15'} \]

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