Why does polygons exterior angles equal 360 degrees?

Answer 1

Let's assume our polygon is a n-gon with n sides. So, there are an equal number of interior and exterior angles.

We know that:


1 Exterior + 1 Interior = will give us 180º

\ \ ________________\___________


Side of a trapezium using symbols.
Thus, the total of the exterior angles and interior angles will be 180nº [a]


As we know, the formula for the sum of interior angles is 180(n-2)º [b]


Subtracting [a] from [b], we get


180n - 180(n-2)


This can be simplified to


180(n-n+2)


Again, we can simplify that to


180*2


which gives us


360º


Thus, we have proved that the exterior angles of any polygon always equal 360º, no matter the number of sides.