Question

Is there a regular polygon with an interior angle sum of 9000°, if so, what is it

Answer 1

Every regular polygon has its exterior angles summing to \(360^\circ\). Take a regular polygon with \(n\) sides, then each exterior angle has measure \(\dfrac{360^\circ}{n}\).

Each interior angle is supplementary to its adjacent exterior angle, i.e. each interior angle measures \(180^\circ-\dfrac{360^\circ}{n}\). With \(n\) total angles, this means the sum of interior angles must be \(180^\circ n-360^\circ\).

Is there some integer value of \(n\) such that
\[180n-360=9000~~?\]