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Prove that the sum of the interior angles of a convex n-gon is (n-2)-180°. (A convex n-gon is a polygon with n sides for which each interior angle is less than 180°.) Hint: start with (k+1)-gon and divide it up into a k-gon and a triangle. 7. Bonus: Given a square, you can cut the square into smaller squares by cutting along lines parallel to the sides of the original square (these lines do not need to travel the entire side length of the original square). For example, by cutting along the lines below, you will divide a square int smaller squares:

Prove that the sum of the interior angles of a convex n-gon is (n-2)-180°. (A convex n-gon is a polygon with n sides for which each interior angle is less than 180°.) Hint: start with (k+1)-gon and divide it up into a k-gon and a triangle. 7. Bonus: Given a square, you can cut the square into smaller squares by cutting along lines parallel to the sides of the original square (these lines do not need to travel the entire side length of the original square). For example, by cutting along the lines below, you will divide a square int smaller squares:

Advanced Engineering Mathematics
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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Prove that the sum of the interior angles of a convex n-gon is (n – 2) - 180°. (A convex n-gon is a polygon with n sides for which each interior angle is less than 180°.) Hint: start with (k +1)-gon and divide it up into a k-gon and a triangle. 7. Bonus: Given a square, you can cut the square into smaller squares by cutting along lines parallel to the sides of the original square (these lines do not need to travel the entire side length of the original square). For example, by cutting along the lines below, you will divide a square intS smaller squares:
Transcribed Image Text:Prove that the sum of the interior angles of a convex n-gon is (n – 2) - 180°. (A convex n-gon is a polygon with n sides for which each interior angle is less than 180°.) Hint: start with (k +1)-gon and divide it up into a k-gon and a triangle. 7. Bonus: Given a square, you can cut the square into smaller squares by cutting along lines parallel to the sides of the original square (these lines do not need to travel the entire side length of the original square). For example, by cutting along the lines below, you will divide a square intS smaller squares:
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