Solution:

According to the question, 2π/5 radians is the difference between two acute angles of a  given right-angled triangle.

We know that

π rad = 180°

In terms of degrees, we can write => 1 rad = 180°/ π

here, the angle is 2π/5

So, using the above relation we have:

(2π/5 × 180/ π) ^o

Putting the value of π = 22/7 in above equation, we get:

$ =\left( 2\times 22/\left( 7\times 5 \right)\times 180/22\times 7 \right) $

$ =\left( 2/5\text{ }\times \text{ }180 \right)\text{ }{}^\circ  $

$ =72{}^\circ  $

Let the measure of one acute angle be x°. Then the other acute angle will be 90° – x°.

Therefore, we can write:

$ x{}^\circ -\left( 90{}^\circ -x{}^\circ  \right)=72{}^\circ  $

$ 2x{}^\circ -90{}^\circ =72{}^\circ  $

$ 2x{}^\circ =72{}^\circ +90{}^\circ  $

$ 2x{}^\circ =162{}^\circ  $

$ x{}^\circ =162{}^\circ /\text{ }2 $

$ x{}^\circ \text{ }=\text{ }81{}^\circ  $

$ 90{}^\circ -x{}^\circ \text{ }=\text{ }90{}^\circ -81{}^\circ  $

$ 90{}^\circ -x{}^\circ =\text{ }9{}^\circ  $

Therefore, the acute angles are 81^o and 9^o