Question

The angles of a quadrilateral are in AP, and the greatest angle is double the least. Express the least angle in radians.

Answer 1

Let the smallest term be x, and the largest term be 2x 

Then AP formed= x, ?, ?, 2x 

So,

s_n = n/2[2a + (n - 1) d]

s_n = n/2[a + (a + (n - 1)d)] = n/2

[From term + (last term)]

360°= 4/2 [x+ 2x]....[We know that → a+(n-1) d= last term= 2x] 

⇒ 180°= 3x 

⇒ x= 60° 

Now, 60° is least angle. 

= 60°= π/180° × 60° 

⇒ 60° = π/3 rad