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Let three angles be a,a+d,a+2d If they are in AP, a+a+d+a+2d=180. Therefore, a+d=60. also, given that a+2d=2a Hence, a=2d Therefore, 3d=60 and d=20. and a=60-d=60-20=40 therefore, 1st angle is a =40 2nd is a+d=40+20=60 3rd is a+2d=40+40=80

Let the least angle be a and the next be a+d and the largest be a+2d The series: a, a+d, a+2d we know that the largest angle is twice the smallest ⇒ a+2d = 2a ⇒ 2d = 2a - a ⇒ 2d = a ⇒ d = a/2 -------------(1) The series: a, a+a/2 , a+2a/2 = a, a+a/2 , a+a These are the angles in a triangle ⇒ a+a+a/2 + a+a = 180 ⇒ (2a+2a+a+2a+2a)/2 = 180 ⇒ 9a = 180×2 ⇒ 9a = 360 ⇒ a = 360/9 ⇒ a = 40 substitute a = 40 in (1) d = a/2 d = 40/2 ∴ d = 20 The series: a, a+d, a+2d = 40, 40+20 , 40+(2×20) = 40, 60, 80 are the angles of a triangle