Which of the following pair of angles are supplementary?

Options

A. `48^(@) , 42^(@)`
B. `60^(@) , 60^(@)`
C. `75^(@) , 105^(@)`
D. `179^(@) , 2^(@)`

Answer

To determine which pair of angles are supplementary, we need to check if the sum of each pair equals 180 degrees. Let's analyze the options one by one.

### Step-by-Step Solution:

1. **Option A: 48 degrees and 42 degrees**
- Calculate the sum:
\[ 48 + 42 = 90 \text{ degrees} \]
- Since 90 degrees is not equal to 180 degrees, this pair is **not supplementary**.

2. **Option B: 60 degrees and 60 degrees**
- Calculate the sum:
\[ 60 + 60 = 120 \text{ degrees} \]
- Since 120 degrees is not equal to 180 degrees, this pair is **not supplementary**.

3. **Option C: 75 degrees and 105 degrees**
- Calculate the sum:
\[ 75 + 105 = 180 \text{ degrees} \]
- Since 180 degrees is equal to 180 degrees, this pair **is supplementary**.

4. **Option D: 179 degrees and 2 degrees**
- Calculate the sum:
\[ 179 + 2 = 181 \text{ degrees} \]
- Since 181 degrees is not equal to 180 degrees, this pair is **not supplementary**.

### Conclusion:
The only pair of angles that are supplementary is **Option C: 75 degrees and 105 degrees**.

---