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Math Expert V
Joined: 02 Sep 2009
Posts: 58415
The diagonal of a polygon is a line segment from any vertex to any non  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 48% (01:14) correct 52% (01:16) wrong based on 64 sessions

HideShow timer Statistics The diagonal of a polygon is a line segment from any vertex to any non-adjacent vertex. The diagram below shows a regular decagon, a 10-sided polygon, with two diagonals drawn. How many possible diagonals does the regular decagon have?

A. 90
B. 80
C. 70
D. 45
E. 35

Attachment: GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg [ 11.86 KiB | Viewed 833 times ]

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Senior Manager  P
Joined: 15 Feb 2018
Posts: 366
The diagonal of a polygon is a line segment from any vertex to any non  [#permalink]

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2
The formula for diagonals in a polygon is $$\frac{n(n-3)}{2}$$

The formula can be derived. Select a point. You can't send a diagonal to its left neighbour, it's right neighbour, or itself (this is the n-3)
There are n points from which the diagonals can originate
So we have n(n-3) [vertices·diagonals from a vertex]

A diagonal sent from x to y is the same as the diagonal from y to x. So we need to put a denominator of 2.

$$\frac{n(n-3)}{2}$$

$$\frac{10(7)}{2}$$=35=E

Originally posted by philipssonicare on 28 Jan 2019, 01:19.
Last edited by philipssonicare on 28 Jan 2019, 03:28, edited 2 times in total.
GMAT Club Legend  D
Joined: 18 Aug 2017
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Location: India
Concentration: Sustainability, Marketing
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Re: The diagonal of a polygon is a line segment from any vertex to any non  [#permalink]

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Bunuel wrote: The diagonal of a polygon is a line segment from any vertex to any non-adjacent vertex. The diagram below shows a regular decagon, a 10-sided polygon, with two diagonals drawn. How many possible diagonals does the regular decagon have?

A. 90
B. 80
C. 70
D. 45
E. 35

Attachment:
GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg

formula to count the no of diagonal in a polygon ; n ( n-3)/2
10 * 7 / 2= 35
IMO E
Intern  B
Joined: 10 Feb 2019
Posts: 4
Re: The diagonal of a polygon is a line segment from any vertex to any non  [#permalink]

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I followed an unconventional way by manipulating the answer choices.

A diagonal needs 2 points and we have 10 points. Total ways to pick 2 points from 10 is $$10 C_2$$ = 45
Now we know that we cannot select adjacent points. So the total number should be less than 45. Hence, 35. (Only one choice available) Re: The diagonal of a polygon is a line segment from any vertex to any non   [#permalink] 19 Feb 2019, 19:22
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