SOLUTION: There is a famous theorem in Euclidean geometry that states that the sum of the interior angles of a triangle is 180. (a) Use the theorem about triangles to determine the sum of

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Question 562200: There is a famous theorem in Euclidean geometry that states that the sum of
the interior angles of a triangle is 180.
(a) Use the theorem about triangles to determine the sum of the angles of
a convex quadrilateral.
(b) Use the result in Part (1) to determine the sum of the angles of a convex
pentagon.
(c) Use the result in Part (2) to determine the sum of the angles of a convex
hexagon.
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
a) Quadrilateral can be divided into two triangles (each with vertices at the vertices of the quadrilateral) so the sum of the angles is 2*180 = 360

b) Same logic as a) but now we can divide into three triangles --> 3*180 = 540

c) 4*180 = 720

We can generalize to n sides and derive the sum of the angles of an n-gon to be 180(n-2).
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