The angles of a quadrilateral are in AP, and the greatest angle is dou

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

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

Answer»

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