: Let a - d, a, a + d be the three angles of the triangle that form AP.
Given that the greatest angle is double the least.
Now, a + d = 2(a - d)
2a - 2d = a + da = 3d …… (1)
Now by angle sum property, (a - d) + a + (a + d) = 180°
3a = 180°
a = 60° …… (2)
From (1) and (2),
3d = 60°
d = 20°
Now, the angles are, a - d = 60°- 20° = 40°
a = 60°
a + d = 60° + 20° = 80°.
Therefore the required angles are 40° 60° 80°
