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# The greatest number of diagonals that can be drawn from one vertex of

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Math Expert
Joined: 02 Sep 2009
Posts: 46284
The greatest number of diagonals that can be drawn from one vertex of [#permalink]

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19 Sep 2017, 23:47
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88% (00:17) correct 13% (00:25) wrong based on 24 sessions

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The greatest number of diagonals that can be drawn from one vertex of a regular six sided polygon is

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

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Re: The greatest number of diagonals that can be drawn from one vertex of [#permalink]

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20 Sep 2017, 06:14
Bunuel wrote:
The greatest number of diagonals that can be drawn from one vertex of a regular six sided polygon is

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Drawing a regular hexagon.
We see that the greatest no. of diagonals can be 3.

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The greatest number of diagonals that can be drawn from one vertex of [#permalink]

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20 Sep 2017, 07:02
Bunuel wrote:
The greatest number of diagonals that can be drawn from one vertex of a regular six sided polygon is

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

It's probably easier to draw and count with this small number of sides.

But if the number of sides were greater (36? ugh), it would be better to know that

The number of diagonals that can be drawn from one vertex of a regular n-sided polygon is (n - 3)

That formula underlies the formula for the total number of diagonals for a regular n-sided polygon:$$\frac{n(n-3)}{2}$$

(n - 3) makes sense. There are as many vertices as there are sides.

To draw a diagonal, you cannot include three vertices in the count of diagonals from one vertex to another: the vertex from which you start (there is no "other" vertex) and the two adjacent vertices (those are sides). There are n vertices. Hence (n - 3).

So from one vertex of a regular six-sided polygon, you can draw (6 - 3) = 3 diagonals

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The greatest number of diagonals that can be drawn from one vertex of   [#permalink] 20 Sep 2017, 07:02
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