\(\frac{\pi}{2}\) radians = \(\frac{180^\circ}{2} = 90^\circ\) Let the smaller angle be \(x^\circ\) Then, the other angle is \((x + 40)^\circ\) So, \[ x + (x + 40) = 90 \Rightarrow 2x + 40 = 90 \Rightarrow 2x = 50 \Rightarrow x = 25 \] Therefore, the two angles are \(25^\circ\) and \(25^\circ + 40^\circ = 65^\circ\) We know that \(180^\circ = \pi\) radians So, \[ 25^\circ = \frac{\pi \times 25}{180} = \frac{5\pi}{36} \text{ radians} \] and \[ 65^\circ = \frac{\pi \times 65}{180} = \frac{13\pi}{36} \text{ radians} \] Hence, the radian measures of the two angles are \(\frac{5\pi}{36}\) radians and \(\frac{13\pi}{36}\) radians.