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How many interior diagonals does a regular nine-sided polygon have? (An $\emph{interior diagonal }$ is a segment connecting two vertices which do not have an edge between them.)

 Mar 25, 2020
 #1
avatar+1970 
+2

Equation:

 

# of diagnols+9=(9×8)/(2×1)=36.

 

Therefore, number of diagonals=36–9=27.

 

Hope this helped!

 Mar 25, 2020
 #2
avatar+111330 
+1

Nice work, Cal.....!!!

 

By the way......there is a formula  for this.......the  nuber  of interior diagonals  =

 

n (n - 3)    / 2        where n is the number  of sides

 

So....in our  case......the number  is

 

9 ( 9 - 3)  / 2    =

 

9 (6)  / 2  = 

 

54 /  2    =

 

27   .......just as Cal found   !!!!!

 

 

cool cool cool

 Mar 25, 2020
 #3
avatar+1970 
+2

Very true! Nice work to you, too, Chris!

CalTheGreat  Mar 25, 2020

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