SOLUTION: solve a regular polygon of (2x+1) sides has 140 as the size of each interior angle, find x.
Algebra.Com
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.
--------------
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.
RELATED QUESTIONS
A regular polygon of (2k+1)sides has 140 as the size of each interior angle. Find... (answered by richard1234)
A regular polygon of(2k +1)sides has 140 as d size of each interior angle.find... (answered by hammy)
a regular polygon has 34 sides, find the size of each interior angle?
(answered by srinivas.g)
A regular polygon has 27 sides. Find the size of each interior... (answered by Alan3354)
A regular polygon has 35 sides. what is the size of each interior... (answered by fcabanski)
A regular polygon has 35 sides. what is the size of each interior... (answered by Earlsdon)
A regular polygon has 33 sides. what is the size of each interior... (answered by Alan3354)
A regular polygon has 34 sides. whats the size of each interior... (answered by ewatrrr)
A regular polygon has 34 sides what the size of each interior... (answered by stanbon)