Question

The angles of a 9 sided polygon are in AP . Which degree measure is always a term of the series

Answer 1

let d be the common difference of the angles in AP.
We know sum of interior angles of a polygon is(n-2)X180degree;where n is number of sides of the polygon
here n=9;so angle sum is 1260degree
we can equate the sum (n/2)X(2a+(n-1)d) to 1260
here n=9,so 2a+8d=280(from the above eqation)
so, a+4d=140.
a is a term which will always be in the AP.
If we know the common difference,we can substitute it on the above equation to get the value of a.