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

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(35256) (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

So in this case

Also, remember that since the sum of the interior and exterior angle is 180

Solve for "y"

Plug in

Multiply EVERY term by "n" to clear the fraction

Distribute

Subtract 180n from both sides.

Divide both sides by -n to isolate x (which is the exterior angle)

Reduce

So this shows that for any regular n-gon, the exterior angle will be
Answer by gonzo(654) (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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