THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.

let the angles be a,a+d,a+2d.

Let a+2d be the greatest.

Then, a+2d=2a

which implies, 2d=a

now, a+a+d+a+2d=180

so 3a+3d=180

so a + d = 60

2d+d=60

d=20

which implies a = 40

so the angles are 40, 60, 80.

Hope u understood.. :D

let the least angle be x

then the other angles are x+d and x+2d

where d is the common difference

x+x+d+x+2d=180^o

3x+3d=180^o

x+d=60

d=60-x  ---------(1)

here the largest angle is x+2d

by the data

x+2d=2x

->d=x/2 -----------(2)

(1) and (2) gives,

60-x=x/2

x=40^o

d= 40/2=20

thus the angles are 40^o,60^o,80^o

40^o+60^o+80^o=180^o

Hope it helps.

let the angles be a,a+d,a+2d.

Let a+2d be the greatest.

therefore, a+2d=2a

thus, 2d=a

, a+a+d+a+2d=180

so 3a+3d=180

 a + d = 60

2d+d=60

d=20

therfore a = 40

so the angles are 40, 60, 80.

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