SOLUTION: This proof cannot be solved in the traditional two-column proof fashion. It has to be solved in an algebraic manner starting with an equation. Prove this theorem: One exterior angl

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Question 163744: This proof cannot be solved in the traditional two-column proof fashion. It has to be solved in an algebraic manner starting with an equation. Prove this theorem: One exterior angle for a regular polygon is 360/n, where n is the number of sides. Please help!
Found 2 solutions by jim_thompson5910, gonzo:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=measure of exterior angle and y = measure of interior angle

We know that the formula for the interior angle is interior_angle=180%28n-2%29%2Fn

So in this case y=180%28n-2%29%2Fn

Also, remember that x%2By=180 since the sum of the interior and exterior angle is 180

y=180-x Solve for "y"


180%28n-2%29%2Fn=180-x Plug in y=180%28n-2%29%2Fn


180%28n-2%29=180n-xn Multiply EVERY term by "n" to clear the fraction


180n-360=180n-xn Distribute


-360=-xn Subtract 180n from both sides.


-360%2F%28-n%29=x Divide both sides by -n to isolate x (which is the exterior angle)


x=360%2Fn Reduce


So this shows that for any regular n-gon, the exterior angle will be 360%2Fn

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
prove that one exterior angle of the polygon is 360/n.
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sum of the interior angles of a polygon is given by the equation sum of i = (n-2)*180.
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since a polygon of n sides has n interior angles, then each interior angle measures ((n-2)*180)/n so the formula for an interior angle is
i = ((n-2)*180)/n
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each exterior angle is a supplement of each interior angle, so each exterior angle measure 180 - ((n-2)*180)/n) so the formula for an exterior angle is
e = 180 - ((n-2)*180)/n)
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multiplying both sides of the equation by n we get
n*e = n*(180-((n-2)*180)/n)
which becomes
n*e = 180*n - (180*n - 360)
removing parentheses this equation becomes
n*e = 180*n - 180*n + 360)
combining like terms this becomes
n*e = 360
dividing both sides of the equation by n make it
e = 360/n
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