Question 1133816
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.