How do you prove that the sum of the interior angles of a convex polygon with n sides is (n-2)*180 degrees using inductive reasoning?
Answer 1
Kelly Adams
To prove this, use mathematical induction. Base case: For a triangle (n=3), the sum is 180 degrees. Inductive step: Assume true for n=k. For n=k+1, divide the polygon into a triangle and a k-sided polygon, proving the formula holds for n=k+1. Thus, by induction, the sum of interior angles of an n-sided convex polygon is (n-2)*180 degrees.
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