Answer: The sum of the exterior angles of a polygon is always 360 degrees. This is because when you travel around the exterior of a polygon, you make one complete revolution of 360 degrees.
To find the measure of each exterior angle of a regular n-gon (a polygon with n sides and angles of equal measure), you divide the total sum of the exterior angles (360 degrees) by the number of sides or angles in the polygon.
So for a regular 100000-gon, each exterior angle measures 360/100000 = 0.0036 degrees.
To find the sum of all the exterior angles in a 100000-gon, we multiply the measure of one exterior angle by the number of exterior angles (which is also equal to the number of sides/vertices in the polygon).
The number of exterior angles in a 100000-gon is also 100000, so:
Sum of exterior angles = 0.0036 degrees/angle × 100000 angles = 360 degrees
Therefore, the sum of the exterior angles of a 100000-gon is 360 degrees.
Explanation: