SOLUTION: how many degrees are the exterior angles of a 25-gon

Question 363101: how many degrees are the exterior angles of a 25-gon
Found 2 solutions by Alan3354, CharlesG2:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
360 total, for all polygons.
360/25 = 14.4 each for a regular 25-gon

Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
"how many degrees are the exterior angles of a 25-gon"
if a regular polygon with all sides equal, then all internal angles will be equal, then also all external angles will be equal

25 sides = 25 vertices
internal angles = (n - 2)*180 = (25 - 2)*180 = 23 * 180 = 4140 degrees
sum of angles at the vertices = 180n = 180 * 25 = 4500 degrees
sum external angles = 4500 - 4140 = 360 degrees
each internal angle = 4140/25 = 165.6 degrees
each external angle = 180 - 165.6 = 14.4 degrees

A polygon with n sides has n - 2 triangles making it up, these triangles are made by drawing non-intersecting diagonals between the vertices (the corners) of the polygon.
n sides = n-gon = n - 2 triangles,
internal angles = (n - 2) * 180 = 180n - 360
n-gon has n vertices
n * 180 = 180n
180n - (180n - 360) = 180n - 180n + 360 = 360 = sum of the external angles
therefore all polygons have 360 degrees as the sum of their external angles

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