Let's carefully convert the given angle from radians to degrees step by step.
Given:
[tex]\[ \frac{7 \pi}{4} \text{ radians} \][/tex]
We know that radians can be converted to degrees using the conversion factor:
[tex]\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \][/tex]
Using this conversion factor, we can find the angle in degrees:
[tex]\[ \left(\frac{7 \pi}{4}\right) \times \frac{180}{\pi} \][/tex]
Notice that the [tex]\(\pi\)[/tex] terms will cancel each other out:
[tex]\[ \left(\frac{7 \pi}{4}\right) \times \frac{180}{\pi} = \frac{7 \times 180}{4} \][/tex]
Now we simplify the fraction:
[tex]\[ \frac{7 \times 180}{4} = \frac{1260}{4} = 315 \text{ degrees} \][/tex]
Therefore, the given angle [tex]\(\frac{7 \pi}{4}\)[/tex] radians is equivalent to [tex]\(\boxed{315 \text{ degrees}}\)[/tex].
