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Consider a regular 23-gon. How many diagonals does the regular polygon have?

 Mar 11, 2020
 #1
avatar+12269 
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Consider a regular 23-gon. How many diagonals does the regular polygon have?

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 Mar 11, 2020
 #2
avatar+25215 
+2

Consider a regular 23-gon. How many diagonals does the regular polygon have?

 

\(\begin{array}{|rcll|} \hline \text{diagonals} &=& (22+ 21+20+\ldots+3+2+1) - 23 \\ &=& \dfrac{1+22}{2}*22 - 23 \\ &=& 23*11 - 23 \\ &=& 23*10 \\ \mathbf{\text{diagonals}} &=& \mathbf{230} \\ \hline \end{array} \)

 

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 Mar 12, 2020

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