In a closed polygon, there are 35 diagonals. How many sides does the polygon have?

Answer: 10

ant101
Jun 3, 2018

#1**+2 **

Hello, again Ant101!

The formula to find the number of diagonals in a closed polygon is: \(\frac{n(n-3)}{2}\) , where n is the number of sides.

Since there are 35 diagonals in the polygon, we can let the above formula equal 35.

So, we have: \(\frac{n(n-3)}{2}=35\)

Taking 2 to the other side, we have: \(n(n-3)=70\)

We need to find a value of n that suits this scenario, therefore \(\boxed{10}\) sides is our answer!

Check: 10*(10-3)=70, 10*7=70, yep!

tertre
Jun 3, 2018