To convert an angle from radians to degrees, you can use the conversion formula:
[tex]\[ \text{Degrees} = \text{Radians} \times \left(\frac{180}{\pi}\right) \][/tex]
Given the angle [tex]\(\frac{4 \pi}{3}\)[/tex] radians, let's use this formula step-by-step:
1. Express the given radian measure:
[tex]\[ \text{Radians} = \frac{4 \pi}{3} \][/tex]
2. Apply the conversion factor:
[tex]\[ \text{Degrees} = \frac{4 \pi}{3} \times \left(\frac{180}{\pi}\right) \][/tex]
3. Simplify the expression:
- First, multiply the numerators and denominators:
[tex]\[ \text{Degrees} = \frac{4 \pi \times 180}{3 \pi} \][/tex]
- Next, cancel out the [tex]\(\pi\)[/tex] in the numerator and denominator:
[tex]\[ \text{Degrees} = \frac{4 \times 180}{3} \][/tex]
- Now, perform the division:
[tex]\[ \text{Degrees} = \frac{720}{3} \][/tex]
[tex]\[ \text{Degrees} = 240 \][/tex]
Thus, the angle [tex]\(\frac{4 \pi}{3}\)[/tex] radians is equal to [tex]\(240^\circ\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{240^\circ} \][/tex]
