The angles of a quadrilateral are in A.P.If the greatest angle is double of the smallest angle,find all the four angles.
Answers
Answer:
Step-by-step explanation:
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.