Question

Is it possible to have a polygon whose sum of interior angles is $2880°$

Answer 1

Sum of interior angles of any polygon of sides $n$is given by $\left(n-2\right)\times 180°$

So, $$\begin{gathered} \left(n-2\right)\times 180°=2880° \\ n-2=\frac{2880}{180} \\ n-2=16 \\ n=18 \end{gathered}$$

The number of sides in a polygon is always a natural number.

Since we get the value of $n$ as natural number, it is possible to have a polygon whose sum of interior angles is $2880°$

So it is a $18$ sided polygon.

Hence, it is possible to have a polygon whose sum of interior angles is $2880°$