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.
If you multiply 360 by the number of angles in the polygon and then subtract the sum of all the interior angles you will end up with the sum of all the exterior angles of the polygon.
A Regular Polygon
A triangle
The sum of the exterior angles of all polygons equals to 360⁰.Since only the sum of the interior angles of all quadrilaterals equals to 360⁰, the polygon must have 4 sides.
(number of sides-2)*180 = sum of interior angles of a polygon
the sum of the interior angles of a 3 sided polygon is = 180 degrees. the sum of the interior angles of any polygon is given by 540/n. in this case n is = 3
(number of sides-2)*180+360 = total sum of interior and exterior angles of any polygon.
The sum of the interior angles of an n-sided polygon is 180n - 360 degrees.
(number of sides-2)*180 = sum of the interior angles
The sum of all the interior angles of a polygon with n sides is (n-2)*180 degrees.
a convex polygon has 6 sides . What is the sum of the measure of its interior angles?
It is: (n-2)*180 = sum of interior angles whereas 'n' is the number of sides of the polygon