Answer :

Given:


Interior angles of a polygon are in A.P


Smallest angle = a = 52°


Common difference = d = 8°


Let the number of sides of a polygon = n


Angles are in the following order


52°, 52° + d, 52° + 2d, ........, 52° + (n - 1) ×d


Sum of n terms in A.P = s


Sum of angles of the given polygon is


Hint:


Sum of interior angles of a polygon of n sides is


Therefore,



180n - 360 = 52n + n (n - 1) ×4


4n2 + 48n = 180n - 360


4n2 - 132n + 360 = 0


n2 - 33n + 90 = 0


(n - 3)(n - 30) = 0


n = 3 &n = 30


It can be a triangle or a 30 sided polygon.


The number of sides of the polygon is 3 or 30.


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