\[ \frac{2\pi}{5} = \frac{2 \times 180^\circ}{5} = 72^\circ \] In a right-angled triangle, the sum of the two acute angles is \(90^\circ\). Let the smaller angle be \(x^\circ\). \(\therefore\) The other angle is \((x + 72)^\circ\) So, \[ x + x + 72 = 90 \Rightarrow 2x + 72 = 90 \Rightarrow 2x = 18 \Rightarrow x = 9 \] \(\therefore\) The two angles are \(9^\circ\) and \((9 + 72)^\circ = 81^\circ\) We know that \(180^\circ = \pi\) radians \[ \therefore 9^\circ = \frac{\pi \times 9}{180} = \frac{\pi}{20} \text{ radians} \quad \text{and} \quad 81^\circ = \frac{\pi \times 81}{180} = \frac{9\pi}{20} \text{ radians} \] \(\therefore\) The measures of the two angles are: - In radians: \(\frac{\pi}{20}\) and \(\frac{9\pi}{20}\) - In degrees: \(9^\circ\) and \(81^\circ\)