The angles of a quadrilateral are in AP .The greatest angle is double the least .find all the angles

The angles of a quadrilateral are in AP .The greatest angle is double

1.	The angles of a quadrilateral are in AP .The greatest angle is double the least .find all the angles
Answer» 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)\xa0The common difference in A.P. = d\xa0Therefore, the sum of the four angles should be equal to that of 360°\xa0Hence, (x-3d)+(x-d)+(x+d)+(x+3d)=360°\xa04x=360°\xa0x=90°\xa0Let (x+3d) be more than (x-3d)\xa0Putting x = 90 degree in the equation x+3d = 2 (x-3d)\xa0Then, 90+3d = 2 (90-3d)\xa09d=90;d=10\xa0Hence, the common difference is 10\xa0Therefore putting the value of x=90° and d=10 in (x-3d)+(x-d)+(x+d)+(x+3d)=360°\xa0The angles are 60, 80, 100, and 120 of the quadrilateral. which are in AP.