180x(N-2)(interior angle)
All polygon of the sums of exterior angles is 360. (if convex)
Chat with our AI personalities
A polygon that has a sum of 2520 degrees of interior angles has 16 sides
The easiest way to solve this is to use the exterior angles of the polygon. The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o. As the polygon is regular, all the interior angles are the same and all the exterior angles are the same. So, for an interior angle of 172o the exterior angle is 180-172 = 8o. The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45. Thus the polygon with interior angles of 172o has 45 sides.
The sum of the interior angles of a polygon with n sides is 180o × (n - 2), consequently the sum of the interior angles of a 28-sided polygon is 4680o (180o × 26).
The sum of what of a 92 sided polygon? The lengths of the sides? The exterior angles? The interior angles?
A polygon with 50 sides, given the sum of all the interior angles in 8640.