The sum of the measures of the interior angles of an n -gon is (n-2)180.
This theorem tells us that the sum of the measures of the interior angles of an n-gon is (n-2)180.
We are given that the sum of the measures of the interior angles is 2880.
(n-2)180= 2880
Let's solve the above equation to find n.
We found that n=18. This means that the polygon with the given measures has 18 sides.
Extra
More About the Polygon Angle-Sum Theorem
The Polygon Interior Angles Theorem states that the sum of the measures of the interior angles of a polygon is given by the following formula.
(n-2)* 180^(∘)
In the formula, n is the number of sides the polygon has.
We can see that the sum of the interior angle measures of a polygon depends on the number of sides the polygon has. Therefore, we just need to know how many sides a polygon has in order to find the sum of the measures of its interior angles.
