Let us start with the explanation:
A rule of polygons says that the sum of the exterior angles always equals 360 degrees.
First of all we need to know the <em>Interior and Exterior angle</em> formulas:
It says the sum of the measures of the interior angles of a polygon with sides is .
Now If we count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.
Let's talk about Hexagon first : It has got 6 sides so, .
Since the skater is going around the hexagon, we need to find the sum of the measure of exterior angles ,
Talking about <em>Octagon</em>, it has got 8 sides so, . So the sum of the measure of exterior angles is:
Plugging the value of 'n' we get:
Now, finding the sum of measure of exterior angles for a sided polygon. We get:
Therefore, when the skater goes around a hexagon he covers , when he goes around an octagon he covers , and when he goes around a regular sided polygon , he covers .