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How many diagonals does a regular 20-sided polygon have?

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Senior Manager
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Joined: 20 May 2014
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How many diagonals does a regular 20-sided polygon have? [#permalink] New post 26 Oct 2017, 23:40
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Question Stats:

66% (00:00) correct 33% (01:19) wrong based on 3 sessions
How many diagonals does a regular 20-sided polygon have?

(A) 60

(B) 120

(C) 170

(D) 240

(E) 400


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[Reveal] Spoiler: OA
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Director
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Re: How many diagonals does a regular 20-sided polygon have? [#permalink] New post 27 Oct 2017, 02:41
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We can start by computing the number of ways two points can be chosen from 20 vertices., i.e. \(20C2 = \frac{20!}{18!2!} = 190\).

Then, we have to notice that with this method we have included not only diagonals but also sides of the polygon because sides join vertices too. Thus, we have to subtract 20 sides from 190 and we get our answer 170. Answer C
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Manager
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Re: How many diagonals does a regular 20-sided polygon have? [#permalink] New post 27 Oct 2017, 10:37
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To solve this problem in the exam, better if we learn this formula for calculating the number of diagonals in a regular polygon i.e.
N(N-3)/2 where N is the no. of sides.

Lets take our problem, we are provided 20 sides.Therefore,

N(N-3)/2 = 20(20-3)/2 = 170.
Re: How many diagonals does a regular 20-sided polygon have?   [#permalink] 27 Oct 2017, 10:37
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How many diagonals does a regular 20-sided polygon have?

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