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The angles of a quadrilateral are …

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

Posted by Suchitra Das 5 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 3 months ago

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.

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