Question

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

14
16
18
20

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=(S)/(180)+2\\ \\ n=(2880)/(180)+2\\ \\ n=16+2\\ \\ n=18\ sides`

therefore

the answer is

`18\ sides`