1. The problem is to convert the angle $2\pi$ radians into degrees. 2. The formula to convert radians to degrees is: $$\text{degrees} = \text{radians} \times \frac{180}{\pi}$$ 3. Applying the formula: $$2\pi \times \frac{180}{\pi}$$ 4. We can cancel $\pi$ in numerator and denominator: $$2\cancel{\pi} \times \frac{180}{\cancel{\pi}} = 2 \times 180$$ 5. Multiply the numbers: $$2 \times 180 = 360$$ 6. Therefore, $2\pi$ radians equals $360$ degrees.