SOLUTION: If the measure of one interior angle of regular polygon is 140 degrees how many sides does the polygon have?

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Question 200217: If the measure of one interior angle of regular polygon is 140 degrees how many sides does the polygon have?
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322)   (Show Source): You can put this solution on YOUR website!
From the information given I believe it has 3 sides.
I think it is a obtuse triangle
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
You just need to find the LCM of 140 & 180. This is 1,260, which when divided by 140 (this being a regular polygon, or a polygon with all equal angles and equal sides), gives us a 9-sided polygon, or a NONAGON.

This sum, 1,260, is also the sum of the angles of all the triangles that make up the polygon, and which when divided by 180 (the sum of all angles of a triangle) equals 7 triangles. Add 2 to this number to get the amount of sides the polygon has, which is 9.

Hope you understand this!!
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