SOLUTION: The measure of an interior angle of a regular polygon is 140�. Classify. Regular Polygon by the number of sides

Question 1035730: The measure of an interior angle of a regular polygon is 140�. Classify. Regular Polygon by the number of sides

Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The measure of an interior angle of a regular idregular is 140�. Classify. Regular Polygon by the number of sides
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Exterior angle = 180 - 140 = 40 degs
360/40 = 9 sides

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the interior angle of a polygon can be measured in one of two ways.

(n-2) * 180 / n is equal to the interior angle of a polygon.

180 - 360 / n is equal to the interior angle of a polygon.

we'll do it using the first formula and then do it using the second formula.

using the first formula, you get 140 = (n-2) * 180 / n
multiply both sides of this equation by n to get 140 * n = (n-2) * 180
simplify to get 140 * n = 180 * n - 360
subtract 180 * n from both sides of this equaiton to get 140 * n - 180 * n = - 360.
simplify to get -40 * n = -360.
divide both sides of this equation by -40 to get n = -360 / -40 = 9.

using the second formula, you get 140 = 180 - 360 / n.
subtract 180 from both sides of this equation, you get 140 - 180 = -360 / n
simplify to get -40 = -360 / n
multiply both sides of this equation by n to get -40 * n = -360.
divide both sides of this equation by -40 to get n = -360 / -40 = 9.

the regular polygon is a 9 sided polygon.
i believe it's called a nonagon.
here's a list of all the possible names you ever wanted to know about how to classify regular polygons and probably much more.
http://www.mathsisfun.com/geometry/polygons.html

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