The difference between the two acute angles of a right - angled triangle is 2π5 radians. Express the angles in degrees.
Let θ1 and θ2 be two acute angles of a right angled triangle.
∴ different of acute angles
θ1−θ2=2π5 radians
∵ in a right angled triangle,
θ1+θ2=π2
θ1−θ2=2π5 . . .(i)
θ1+θ2=π2 . . . (ii)
On solving
2θ1=2π5+π2
θ1=9π20
From equation (ii)
θ2=π20
So angles in degrees
θ1=9π20×180π=81∘
and θ2=π20×180π=9∘