Question

the angles of a quadrilateral are in AP. if the greatest angle is double the smallest angle find all the four angles ​

Answer 1

Answer:

The four angles are 60, 80, 100 and 120 of the quadrilateral.

Step-by-step explanation:

The angle of a quadrilateral are in Arithmetic Progression, now as there are four angles, the greatest of all the angles is double to that of smallest angles. Then to find the 4 angles of the quadrilateral,  the angles can be written as (x-3d)(x-d)(x+d)(x+3d)

The common difference in A.P. = d

Therefore, the sum of the four angles should be equal to that of 360°

Hence, (x-3d)+(x-d)+(x+d)+(x+3d)=360°

4x=360°

x=90°

Let (x+3d) be more than (x-3d)

Putting x = 90 degree in the equation x+3d = 2 (x-3d)

Then, 90+3d = 2 (90-3d)

9d=90;d=10

Hence, the common difference is 10

Therefore putting the value of  x=90° and  d=10 in (x-3d)+(x-d)+(x+d)+(x+3d)=360°

The angles are 60, 80, 100, and 120 of the quadrilateral. which are in AP.

Step-by-step explanation: