Question

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 ?

Answer 1

`\text{There is 560 diagonals.}`

Explanation:

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

`\begin{gathered} \text{ \# of diagonals= }(n(n-3))/(2) \\ \end{gathered}`

Therefore, for a 35-sided polygon:

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