Question

the difference between two acute angle of a right angle triangle is π/9 find the angle in degrees

Answer 1

let two acute angles be x and y

the difference between two acute angle of a right angle triangle is π/9
so, x - y = π/9
where π = 180°
x - y = 180°/9
x - y = 20°
x = y + 20°..............(1)

sum of two acute angle is 90
so, x + y = 90°.........(2)

substitute (1) in (2)
y + 20° + y = 90°
2y = 90° - 20°
2y = 70°
y = 70°/2
y = 35°

substitute y in (1)
x = 35° + 20°
x = 55°

so, two acute angles are x = 55° and y = 35°