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(5) Use strong math induction to prove if the sum of the interior angles of a triangle is 180° then the sum of the interior angles of any convex n-gon is (n – 2) · 180°, for all n > 3.

(5) Use strong math induction to prove if the sum of the interior angles of a triangle is 180° then the sum of the interior angles of any convex n-gon is (n – 2) · 180°, for all n > 3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(5) Use strong math induction to prove if the sum of the interior angles of a triangle is 180° then the sum of the interior angles of any convex n-gon is (n – 2) · 180°, for all n > 3. Definition: For n E N,n > 3 a convex n-gon is the n -sided figure created when successive vertices from the set of points {v1, V2, Vn} are connected by non-overlapping segments v,V2, V½V3, ·…, VnVị such that no ... interior angle exceeds 180°, where the interior angles are the angles whose rays are successive sides. Remark: Rectangles, trapezoids, hexagons and octagons are common examples of n -gons. V2 This 4-gon is not convex because the interior angle at V2 is greater than 180°.
Transcribed Image Text:(5) Use strong math induction to prove if the sum of the interior angles of a triangle is 180° then the sum of the interior angles of any convex n-gon is (n – 2) · 180°, for all n > 3. Definition: For n E N,n > 3 a convex n-gon is the n -sided figure created when successive vertices from the set of points {v1, V2, Vn} are connected by non-overlapping segments v,V2, V½V3, ·…, VnVị such that no ... interior angle exceeds 180°, where the interior angles are the angles whose rays are successive sides. Remark: Rectangles, trapezoids, hexagons and octagons are common examples of n -gons. V2 This 4-gon is not convex because the interior angle at V2 is greater than 180°.
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