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How many diagonals does a polygon with 18 sides have if

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Senior Manager
Senior Manager
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Joined: 02 Dec 2007
Posts: 449

Kudos [?]: 278 [0], given: 6

How many diagonals does a polygon with 18 sides have if [#permalink]

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New post 27 Aug 2008, 08:41
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

. How many diagonals does a polygon with 18 sides have if three of its vertices do not send any diagonal? Use the formula: number of diagonals: n (n-3)/2 where n is the number of sides. Each vertex sends of n-3 diagonals.

a) 90
b) 126
c) 210
d) 264
e) 306

Kudos [?]: 278 [0], given: 6

Manager
Manager
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Joined: 22 Jul 2008
Posts: 149

Kudos [?]: 18 [0], given: 0

Re: Diagonal [#permalink]

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New post 27 Aug 2008, 10:45
Each vertex will send off 18-3-3 = 12 diagonals. And there are 15 vertices to take into account. Therefore, the total no. of diagonals = 15 * 12 = 180.
Now each diagonal is shared by 2 vertices. Hence, total no. of diagonals = 180/2 =90.

Kudos [?]: 18 [0], given: 0

Re: Diagonal   [#permalink] 27 Aug 2008, 10:45
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How many diagonals does a polygon with 18 sides have if

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