# The interior angl

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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