I have just learnt permutations, dispositions, combinations. How have the right to I settle it with these concepts? I drew it and also it to be \$35\$ diagonals. How can I prove it through this method?

A diagonal join a crest to among the vertices that perform not include that vertex itself and the immediately surrounding vertices. So: for each vertex over there are seven diagonals. Time 10 equals 70; every diagonal is count twice, for this reason the last answer is 35.

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Now, utilizing combinations and also such: There are \$inom102;\$("10 choose 2") bag of vertices, which amounts to 45. For this reason there room 45 heat segments joining pairs of vertices. Exactly 10 of those room sides of the decagon, the others space diagonals. Answer: 35. (Corrected; original had actually "10 select 9" for no reason various other than my lack of concentration.)

Formula because that calculating variety of diagonals of any polygon the n political parties = n*(n - 3)/2

So here it"s a decagon ,that is a 10 face polygon, therefore n = 10. Simply plug value of n right into the formula , girlfriend get: 10*(10-3)/2 = 35. Ans :)

(Note : no issue what sided polygon the is, you can find any no of diagonals in any type of polygon)

(N-1 select 2 ) -1

Example, (10-1 select 2) -1= (9 choose 2) -1= 36-1= 35 diagonal line lines

This will occupational for any regular shape

Example 2/ 20 sides would certainly be C19,2 -1=170 Check: C20,2 - 20 =170

Very easy formula arisen by Shawn Covrigaru

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