SOLUTION: if doubling the number of sides of a regular polygon increase the angle between adjacent sides by 10 degrees, what is the original number of sides?

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Question 768150: if doubling the number of sides of a regular polygon increase the angle between adjacent sides by 10 degrees, what is the original number of sides?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You could find that calculating the interior angle at each vertex, you would be using equivalent to 180-360%2Fn, which could also be used as 180%281-2%2Fn%29 for the degrees of each interior angle, at a vertex, n being the number of sides in the polygon.

Now, n is an unknown variable.
Doubled number of sides, vertex angle 180(1-2/(2n)) degrees.
Original number of sides, vertex angle (180-2/n).

Their difference is 10 degrees:
highlight%28180%2A%281-2%2F%282n%29%29-180%281-2%2Fn%29=10%29
180-180%2Fn-180%2B360%2Fn=10
-180%2B360=10n
180=10n
highlight%28n=18%29 original sides, to be doubled, giving 10 degree increase at each vertex.