We are given that the sum of the interior angle measures of a polygon with $n$ sides is $2880$ and we want to find $n .$ To do it, recall the Polygon Angle-Sum Theorem.

Polygon Angle-Sum Theorem
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 .

(n - 2) 180 = 2880

DivEqn

$LHS / 180 = RHS / 180$

n - 2 = \frac{2 8 8 0}{1 8 0}

CalcQuot

Calculate quotient

n - 2 = 16

AddEqn

$LHS + 2 = RHS + 2$

n = 18

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) \cdot 18 0^{\circ}

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.

Exercise

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