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

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Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 18

Kudos [?]: 50 [0], given: 220

How many diagonals does a regular 20-sided polygon have? [#permalink]  26 Oct 2017, 23:40
00:00

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

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356 [2] , given: 66

Re: How many diagonals does a regular 20-sided polygon have? [#permalink]  27 Oct 2017, 02:41
2
KUDOS
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
Manager
Joined: 01 Apr 2017
Posts: 61
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 62 [2] , given: 27

Re: How many diagonals does a regular 20-sided polygon have? [#permalink]  27 Oct 2017, 10:37
2
KUDOS
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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