How many degrees is $\frac{2\pi }{9}$ radians?

• A. $80$ degrees
• B. $180$ degrees
• C. $20$ degrees
• D. $40$ degrees

Answer: (A)

Verified step by step guidance

1. Recall the formula to convert radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
2. Identify the given radian measure: \(\frac{2\pi}{9}\) radians.
3. Substitute the radian value into the conversion formula: \(\text{degrees} = \frac{2\pi}{9} \times \frac{180}{\pi}\).
4. Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\text{degrees} = \frac{2 \times 180}{9}\).
5. Calculate the remaining fraction to find the degree measure.