A polygon made up of 360 line segments of same length whose every interior angle is a natural number between 1° and 360° and only occurs once

Question

Is it possible to create this polygon and if so how can I visualise it?

I asked myself this while trying to solve an unrelated mathematical problem taken from a magazine and seemingly lack the knowledge to give myself an answer. Therefore I hope to find one (or more) here.

Answer 1

The average angle in an $n$-sided polygon is ${n-2\over n}180^\circ$. So a $360$-gon has average angle $179^\circ$. The average of the numbers from $1$ to $360$ is $180.5$, so they don't quite work.
To see why the sum of the angles must be $358×180°$, note you can snip off a triangle formed by adjacent edges, leaving a $359$-gon. Repeat that, and you end up with 358 triangles, each has $180°$.