Question

If the sum of a polygon's interior angles is 2880 degrees how much sides must the polygon have?

Answer 1

18 sides

Step-by-step explanation:

The sum of the interior angle of a polygon is determined using the formula:

`\begin{gathered} \text{Sum}=(n-2)180\degree \\ \text{Where n=the number of sides} \end{gathered}`

Therefore, we have that:

`180(n-2)=2880`

Begin solving the equation for n by dividing both sides by 180.

`\begin{gathered} (180(n-2))/(180)=(2880)/(180) \\ n-2=16 \end{gathered}`

Next, add 2 to both sides of the equation:

`\begin{gathered} n-2+2=16+2 \\ n=18 \end{gathered}`

The polygon must have 18 sides.