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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.
What else can I help you with?
What shape equals 360 degrees?
The exterior angles of polygons equal 360 degrees.
Interior and exterior angles of a 30 sided polygon?
The total of the interior angles equal 5040, and each angle measures 168 degrees The total of the exterior angles equal 360, and each angle measures 12 degrees
What polygon does the sum of the measures of interior angles equal the sum of the measures of the exterior angles?
A 4 sided quadrilateral has interior angles that add up to 360 degrees and its exterior angles add up to 360 degrees
What is the exterior angle of an octagon?
The exterior angle of a general octagon is any angle less than 180 degrees. The sum of the exterior angles of a polygon is 360 degrees. If the octagon is regular, then each of its 8 exterior angles is equal to 360/8 = 45 degrees.
What shape has a exterior angle of 45 degrees?
Any shape can have an exterior angle of 45 degrees. If you are talking about exterior angle sum, it is always 360 degrees for any polygon. If you are talking about a regular polygon (equal exterior angles), it would be 360/45=8 sides. Therefore, a regular octagon has exterior angles of 45 degrees.
