SOLUTION: solve a regular polygon of (2x+1) sides has 140 as the size of each interior angle, find x.

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Question 1133816: solve a regular polygon of (2x+1) sides has 140 as the size of each interior angle, find x.
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
solve a regular polygon of (2x+1) sides has 140 as the size of each interior angle, find x.
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Ext angles = 40 degs
360/40 = 9 sides

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
if the internal angle is 140, then the external angle is 180 - 140 = 40 degrees.

the number of sides is therefore 360 / 40 = 9 because 9 * 40 = 360.

therefore 2x + 1 = 9
subtract 1 from both sides to get 2x = 8
divide both sides by 2 to get x = 4.

your solution is x = 4.

the number of sides can also be obtained from the internal angle.

the formula for that is i = 180 * (n - 2) / n

i is the internal angle.
n is the number of sides.

to solve this equation for n, do the following.

multiply both sides of the equation by n to get i * n = 180 * (n - 2)

simplify to get i * n = 180 * n - 360

subtract i * n from both sides of the equation and add 360 to both sides of the equation to get 360 = 180 * n - i * n

factor out the n to get 360 = n * (180 - i)

divide both sides of the equation by n * (180 - i) to get:

360 / (180 - i) = n

since i = 140, this becomes 360 / (180 - 140) = n which becomes 360 / 40 = n which becomes 9 = n.

it's much easier to use the external angle if you can find it.

the external angle is always 180 - the internal angle.

in this case the external angle was 180 - 140 = 40.

the answer is the same as when using the internal angle directly, just easier to derive.

2x + 1 = 9
solve for x to get x = 4.