Question

the angle of a triangle are in A.P, the least being half the greatest.find the angle.

Answer 1

let
the greatest be a+d
the least be a-d=(a+d)/2
the other be a

a+(a+d)/2+a+d=180
2a+d+(a+d)/2=180
(4a+2d+a+d)/2=180
5a+3d=360----------(1)

2a=a+d+(a+d)/2
2a=(2a+2d+a+d)/2
4a=3a+3d
4a-3a=3d
a=3d-------------------(2)

substitute (2) in (1)

5(3d)+3d=360
15d+3d=360
18d=360
d=360/18
d=20

a=3×20=60

the greatest angle is 60+20 = 80
the least angle is 60-20 = 40
the other angle is 60