Question

the sum of the interior angles of a polygon are 2880°. how many sides does it have? what is the name of this polygon?

Explanation:

Step1: Recall the formula for sum of interior angles

The formula for the sum of interior angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides and $S$ is the sum of interior - angles.

Step2: Substitute the given sum into the formula

We are given that $S = 2880^{\circ}$, so we set up the equation $2880=(n - 2)\times180$.

Step3: Solve for $n$

First, divide both sides of the equation by 180: $\frac{2880}{180}=n - 2$. Since $\frac{2880}{180}=16$, the equation becomes $16=n - 2$. Then, add 2 to both sides: $n=16 + 2=18$.

Step4: Name the polygon

A polygon with 18 sides is called an octadecagon.

Answer:

18
Octadecagon