The angles of a triangle are in A.P., the least being half the greatest. Find the angles.

Let the angles be , (a-d) , (a) , (a+d)

Sum of the angles of a triangle is 180^∘

So, (a-d)+(a)+(a+d)=180^∘∙-----(1)

⇒3a=180^∘

⇒a=60^∘

Also, from the given condition,

 60-d=1/2 (60+d)

⇒2(60-d)=60+d

⇒120-2d=60+d

⇒120-60=d+2d

⇒60=3d

⇒d=20^∘

Thus, the required angles are 40^∘, 60^∘, 80^∘