The supplementary angle to $\frac{2 \pi}{5}$ is

Step 1 ：The supplementary angle to an angle is defined as the difference between 180 degrees (or \(\pi\) radians) and the given angle.

Step 2 ：So, to find the supplementary angle to \(\frac{2 \pi}{5}\), we need to subtract \(\frac{2 \pi}{5}\) from \(\pi\).

Step 3 ：\(\text{given_angle} = \frac{2\pi}{5}\)

Step 4 ：\(\text{supplementary_angle} = \pi - \text{given_angle} = \frac{3\pi}{5}\)

Step 5 ：Final Answer: The supplementary angle to \(\frac{2 \pi}{5}\) is \(\boxed{\frac{3 \pi}{5}}\)