# The angle of the triangle are in AP if the greatest angle is twice the least find all the angles

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by harnoor1

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by harnoor1

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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

The Brainliest Answer!

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