How many degrees will the skaters turn if they go once around a regular hexagon? A regular octagon? A regular polygon with #n# sides?

1 Answer
Kalyanam S.
Aug 3, 2018

The sum of the measures of the exterior angles of a polygon is always 360°. For that matter, any closed figure will always account for #360^@#, exception being a triangle which is #180^@#

Explanation:

Interior and exterior angle formulas: The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. The measure of each interior angle of an equiangular n-gon is. If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.

Hexagon : 6 sides

Sum of measure of exterior angles #= (6-2) * 180 = 720^@ = (4pi)^c#

Octogenarian : 8 sides

Sum of measure of exterior angles #= (8-2) * 180 = 1080^@ = (6pi)^c#

Polygon of n sides

Sum of measure of exterior angles #= ((n-2) * 180)^@ = ((n-2)pi)^c#

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