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The diagonal of a polygon is a line segment from any vertex to any non

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The diagonal of a polygon is a line segment from any vertex to any non  [#permalink]

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New post 28 Jan 2019, 00:05
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54% (01:24) correct 46% (01:17) wrong based on 35 sessions

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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
GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg [ 11.86 KiB | Viewed 410 times ]

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The diagonal of a polygon is a line segment from any vertex to any non  [#permalink]

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New post Updated on: 28 Jan 2019, 02:28
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, 00:19.
Last edited by philipssonicare on 28 Jan 2019, 02:28, edited 2 times in total.
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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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New post 28 Jan 2019, 02:09
Bunuel wrote:
Image
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
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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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New post 19 Feb 2019, 18:22
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)
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Re: The diagonal of a polygon is a line segment from any vertex to any non   [#permalink] 19 Feb 2019, 18:22
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