π radians = 180°
\(\frac { \pi }{ 9 }\) radian = \(\frac { 180 }{ \pi } \times \frac { \pi }{ 9 }\) = 20°
Let the two acute angles of the right-angled triangle be x and y (x > y).
Then x + y = 90° …(i)
and x – y = 20° …(ii)
Solving (i) and (ii) we get
2x = 110°
⇒ x = 55°
55° + y = 90°
⇒ y = 35°
Hence, two angles are 55° and 35° respectively.
