Math, asked by harnoor1, 1 year ago

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

Answers

Answered by TarunBansal
622
Let three angles be a,a+d,a+2d
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
Answered by yasummu
294
Let the least angle be a and the next be a+d and the largest be a+2d
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
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