Question

the angles of quadrilateral are in AP and the greatest angle is double the least find angles of a quadrilateral in radian ​

Answer 1

Step-by-step explanation:

a+a+d+a+2d+a+3d = 360°

4a + 6d = 360°

2a + 3d = 180°

a+3d = 2a

a = 3d

3a = 180°

a = 60°

d = 20°

The angles are 60° , 80° , 100° & 120°

Now , angles are π/3 , 4π/9 , 5π/9 , 2π/3 .

Answer 2

Answer:

π/3, 4π/9, 5π/9, 2π/3

Step-by-step explanation:

let the angles of quadrilateral be a-3d, a-d, a+d, a+3d. these 4 are in AP with common difference 2d.

sum of angles is 2π. 4a = 2π.

therefore a=π/2.

given that a+3d = 2(a-3d)

a= 9d

π/2=9d

d=π/18

therefore the angles are π/2 - π/6, π/2 - π/18, π/2 + π/18, π/2 + π/6

π/3, 4π/9, 5π/9, 2π/3