(5) Use strong math induction to prove if the sum of the interior angles of a triangle is 180° then thesum 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 theset 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.V2This 4-gon is not convex because theinterior angle atV2isgreater than 180°.

The sum of interior angles of a triangle is 180 degree. According to the diagram the XY is…

Answered: (5) Use strong math induction to prove…

(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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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°.

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