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# geometry

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

Mar 11, 2020

#1
+11681
+2

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

Mar 11, 2020
#2
+24371
+2

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

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

Mar 12, 2020