Given the difference between the two acute angles of a right-angled triangle is 2π/5 radians.

We know that π rad = 180° ⇒ 1 rad = 180°/ π

Given

= (36 × 2) °

= 72°

Let one acute angle be x° and the other acute angle be 90° - x°.

Then,

⇒ x° - (90° - x°) = 72°

⇒ 2x° - 90° = 72°

⇒ 2x° = 72° + 90°

⇒ 2x° = 162°

⇒ x° = 162°/ 2

∴ x° = 81° and 90° - x° = 90° - 81° = 9°