1)What’s the total number of different diagonals in a 35- sided polygon?2)Each person at a party shook hand with everyone else exactly once. There were 66. Handshakes. How many people were at the party ?

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AriettaO57753 AriettaO57753

31-10-2022
Mathematics

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1)What’s the total number of different diagonals in a 35- sided polygon?2)Each person at a party shook hand with everyone else exactly once. There were 66. Handshakes. How many people were at the party ?

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HannahgraceW661377 HannahgraceW661377 · Answer 1 · 2022-10-31T14:10:28+01:00

Answer:

[tex]\text{There is 560 diagonals.}[/tex]

Step-by-step explanation:

The number of diagonals on a polygon with n number of sides is represented by the following equation:

[tex]\begin{gathered} \text{ \# of diagonals= }\frac{n(n-3)}{2} \\ \end{gathered}[/tex]

Therefore, for a 35-sided polygon:

[tex]\begin{gathered} \text{ \# of diagonals=}\frac{35(35-3)}{2} \\ \text{ \# of diagonals=}560\text{ } \\ \text{There is 560 diagonals.} \end{gathered}[/tex]