Question

Maths Center of Leaming
16a The angles of a triangle are in A.P. The greatest angle is twice the
least. Find all angles of the triangle.​

Answer 1

Answer:

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