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'Integral Polygons' printed from https://nrich.maths.org/
The greatest number of sides the polygon could have is $360$.
As each interior angle of the polygon is a whole number of degrees,
the same must apply to each exterior angle. The sum of the exterior
angles of a polygon is $360^{\circ}$ and so the greatest number of
sides will be that of $360$-sided polygon in which each interior
angle is $179^{\circ}$, thus making each exterior angle
$1^{\circ}$.