A polygon is said to be convex if any line segment connecting two vertices of the polygon lies entirely inside the polygon. A polygon that is not convex is said to be concave. Convex Concave Prove, using induction on the number of vertices in the polygon, that the sum of the interior angles in a convex polygon with n vertices is (n - 2)n. You may assume interesting facts about triangles that you may remember from your past.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A polygon is said to be convex if any line segment connecting two vertices of the polygon lies entirely inside
the polygon. A polygon that is not convex is said to be concave.
Convex
Concave
Prove, using induction on the number of vertices in the polygon, that the sum of the interior angles in a
convex polygon with n vertices is (n - 2)n. You may assume interesting facts about triangles that you
may remember from your past.
Transcribed Image Text:A polygon is said to be convex if any line segment connecting two vertices of the polygon lies entirely inside the polygon. A polygon that is not convex is said to be concave. Convex Concave Prove, using induction on the number of vertices in the polygon, that the sum of the interior angles in a convex polygon with n vertices is (n - 2)n. You may assume interesting facts about triangles that you may remember from your past.
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