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

Answer:

$\text{There is 560 diagonals.}$

Step-by-step explanation:

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

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

Therefore, for a 35-sided polygon:

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