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Turkish
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how many internal diagonals does a decagon (ten sided polygon) have? 27 Feb 2015, 03:18
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D
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25% (medium)

Question Stats:

72% (00:55) correct 28% (01:30) wrong based on 225 sessions

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how many internal diagonals does a decagon (ten sided polygon) have?

A. 90
B. 85
C. 70
D. 35
E. 25
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D
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how many internal diagonals does a decagon (ten sided polygon) have? 27 Feb 2015, 03:30
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how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25
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hi,
the questions means we have to choose two vertices out of 10=10c2..
but these will also contain vertices adjoining to each other as these form sides and not diagonals..
ans=10c2-10=45-10=35
ans D..35
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how many internal diagonals does a decagon (ten sided polygon) have? 28 Feb 2015, 03:20
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how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25
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Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 10
No. of diagonals = 10(10 - 3)/2
= 35
Hence option 4.

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how many internal diagonals does a decagon (ten sided polygon) have? 03 Jan 2019, 09:06
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how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25
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Well I took a different approach:

Square with 4 sides = 2 diagonals
Pentagon 5 sides = 5 diagonals (increase of 3)
Hexagon 6 sides = 9 diagonals (increase of 4)
Septagon 7 side = 14 diagons (increase of 5 from previous)

Hence the diagonals are increasing in a certain orders and their difference increase is a normal AP: 3, 4, 5....so on
Hence for 8 sides = 20
9 sides = 27
10 sides = 35 diagonals

Hence the answer is D
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how many internal diagonals does a decagon (ten sided polygon) have? 05 May 2020, 22:16
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how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25
Show more

Asked: how many internal diagonals does a decagon (ten sided polygon) have?

The number of diagonals = ^nC_2 - n = n(n-1)/2 - n = n(n-3)/2 = 10*7/2 = 35

IMO D
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how many internal diagonals does a decagon (ten sided polygon) have? 15 Oct 2021, 21:45
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Quote:
hi,
the questions means we have to choose two vertices out of 10=10c2..
but these will also contain vertices adjoining to each other as these form sides and not diagonals..
ans=10c2-10=45-10=35
ans D..35
Show more

Dear chetan2u, Could you please help me understand how you have found 10, which you have subtracted from 10c2? You don't know how much you've helped me with my preparation. Thanks a million!
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how many internal diagonals does a decagon (ten sided polygon) have? 16 Oct 2021, 03:40
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sjuniv32
Quote:
hi,
the questions means we have to choose two vertices out of 10=10c2..
but these will also contain vertices adjoining to each other as these form sides and not diagonals..
ans=10c2-10=45-10=35
ans D..35

Dear chetan2u, Could you please help me understand how you have found 10, which you have subtracted from 10c2? You don't know how much you've helped me with my preparation. Thanks a million!
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Glad to hear that.

What you get from 10C2 is choosing 2 vertices from 10 vertices. Thus you will get 10C2 lines.

However, these 10C2 consist of 10 sides of decagon. For example, if ABCDEFGHJK is decagon, then AB, BC, CD, DE, EF, FG, GH, HJ, JK and KA are 10 sides that have to be subtracted.
The remaining are diagonals, that is AC, AD, AE and so on
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