Question

of the three angles of a triangle , one is half the greatest and thrice the smallest . find the angles

Answer 1

let the angle be x
largest is 2x
smallest = x/3
..
x+2x+x/3 =180
3x+6x+x / 3 =180
10x=540
x=54 one angle
largest = 2x= 2*54=108
smallest = x/3 = 18
...
CHECK
54+18+108=180 

Answer 2

Let a - d, a, a + d be the three angles of the triangle that form AP.

Given that the greatest angle is twice the least.

Now, 2(a - d) = a + d

2a - 2d = a + d

a = 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°.