A convex polygon has 13 sides when the interior angle sum is [tex]1980^{0}[/tex].
What is convex polygon?
A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.
Given a convex polygon
For a convex polygon with n sides, the interior angle sum is [tex]180^{0}[/tex] × [tex](n-2)[/tex]
Let [tex]180^{0}[/tex] × [tex](n-2)[/tex] = [tex]1980^{0}[/tex]
⇒ n - 2 = 11
⇒ n = 11 + 2
⇒ n = 13
Thus, a convex polygon has 13 sides when the interior angle sum is [tex]1980^{0}[/tex].
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