What is the measure in degrees of an angle that is `(pi)/(4)` radians?

Options

A. `4^(@)`
B. `25^(@)`
C. `45^(@)`
D. `90^(@)`

Answer

To convert an angle from radians to degrees, we can use the relationship that \( \pi \) radians is equal to \( 180 \) degrees.

### Step-by-Step Solution:

1. **Identify the given angle in radians**:
The angle given is \( \frac{\pi}{4} \) radians.

2. **Use the conversion factor**:
We know that:
\[ \pi \text{ radians} = 180 \text{ degrees} \]

3. **Set up the conversion for \( \frac{\pi}{4} \) radians**:
To convert \( \frac{\pi}{4} \) radians to degrees, we can set up the equation:
\[ \frac{\pi}{4} \text{ radians} = \frac{180 \text{ degrees}}{\pi} \cdot \frac{\pi}{4} \]

4. **Simplify the equation**:
By multiplying, we have:
\[ \frac{180}{4} \text{ degrees} = 45 \text{ degrees} \]

5. **Conclusion**:
Therefore, the measure of the angle \( \frac{\pi}{4} \) radians is equal to \( 45 \) degrees.

### Final Answer:
The measure in degrees of an angle that is \( \frac{\pi}{4} \) radians is \( 45 \) degrees.