wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The interior angles of a polygon are in A.P. the smallest angle is 120o and the common difference is 5o, Find the number of sides of the polygon.

Open in App
Solution

Let the number of sides of the polygon be n Then the sum of all the interior angles =(n×180360) sum of the interior angles.
=120+125+130.... to n terms =n2[240+(n1)5]
n2[240+(n1)5]=n×18003600
n225n+144=0
(n9)(n16)=0
n=9 or 16
But when n=16, the greatest interior angle is 1200+(161)5=1950 which is not possible, for interior angle is<180.Hence the number of sides =9

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Arithmetic Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon