SOLUTION: If exterior angle of a regular polygon is 18 find its number of sides

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Question 892523: If exterior angle of a regular polygon is 18 find its number of sides
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the exterior angles of any convex polygon is 360°.  Since this
is a regular polygon the polygon has all its exterior angles the same, so each
one would be %22360%B0%22%2Fn, so we have the equation:

%22360%B0%22%2Fn%22%22=%22%22%2218%B0%22

Multiply both sides by n

%22360%B0%22%22%22=%22%22%2218%B0n%22

Divide both sides by 18°

%22360%B0%22%2F%2218%B0%22%22%22=%22%22n

20%22%22=%22%22n

So it has 20 sides. The 20-sided polygon is this figure below. Notice 
that the green lines are the extensions of two adjacent sides and the 
angle between those two green lines is an exterior angle of 18°.



Edwin