SOLUTION: In geometry, a convex polygon is a many-sided closed figure, with no sides collapsing in towards the middle. The points where the sides intersect are called vertices and the line s

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Question 1017366: In geometry, a convex polygon is a many-sided closed figure, with no sides collapsing in towards the middle. The points where the sides intersect are called vertices and the line segment joining any two nonconsecutive vertices is called a diagonal of the polygon. The number of diagonals of a polygons is given by the formula D=n(n-3)/2 , where n is the number of sides. Complete parts (a) through (c)
A) calculate the number of diagonals in a heptagon.
D=
B) calculate the number of diagonals in a nonagon.
D=
C) if a polygon has 77 diagonals, how many sides does it have?
N=
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
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In geometry, a convex polygon is a many-sided closed figure, with no sides collapsing in towards the middle. The points where the sides intersect are called vertices and the line segment joining any two nonconsecutive vertices is called a diagonal of the polygon. The number of diagonals of a polygons is given by the formula D=n(n-3)/2 , where n is the number of sides. Complete parts (a) through (c)
A) calculate the number of diagonals in a heptagon.
D=
B) calculate the number of diagonals in a nonagon.
D=
C) if a polygon has 77 diagonals, how many sides does it have?
N=
--------------------------------------------------------- 

A) Heptagon is 7-sided polygon. The number of diagonals for 7-gon is 

    =  = 7*2 = 14.


B) Nonagon is 9-gon (according to Wikipedia). The number of diagonals for 9-gon is

    =  = 9*3 = 27.


C) Solve the quadratic equation

    = 77.

   n = 14.


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