SOLUTION: If a regular polygon has an ecterior angle of 18 degrees, how many sides would that polygon have? and If a regular polygon has an interior angle of 135 degrees, how many sid

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Question 14620: If a regular polygon has an ecterior angle of 18 degrees, how many sides would that polygon have?
and
If a regular polygon has an interior angle of 135 degrees, how many sides would that polygon have?

Please help me
Reanne
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The exterior angle of a regular polygon is the supplement of its interior angle.
The interior angle of a regular polygon is given by:
A+=+%28%28n-2%29180%29%2Fn where: n is the number of sides of the regular polygon.
1) You can write:
180-%28%28n-2%29180%29%2Fn+=+18 simplify and solve for n, the number of sides.
%28180n+-+180n+%2B+360%29%2Fn+=+18 Multiply both sides by n
180n+-+180n+%2B+360+=+18n
360+=+18n Divide both sides by 18.
n+=+20 sides.
2) Use the formula for the interior angle of a regular polygon.
%28%28n-2%29180%29%2Fn+=+135 Simplify and solve for n.
%28180n+-+360%29%2Fn+=+135 Multiply both sides by n
180n+-+360+=+135n Add 360 to both sides.
180n+=+135n+%2B+360 Subtract 135n from both sides.
45n+=+360 Divide both sides by 45
n+=+8 sides.