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