Question

The sum of the measures of the interior angles of a polygon is 2880°. How many sides does the polygon have?

Answer 1

There are 18 sides.....

Answer 2

Let

S------> The sum of the measures of the interior angles of a polygon

n-------> number of sides of a polygon

we know that

The formula to find the sum of the measures of the interior angles of a polygon is equal to

$S=(n-2)*180$°

in this problem

$S=2880$°

Solve for n

$S=(n-2)*180\\ \\ n=\frac{S}{180}+2\\ \\ n=\frac{2880}{180}+2\\ \\ n=16+2\\ \\ n=18\ sides$

therefore

the answer is

$18\ sides$