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this time its a 11-gon
ok so 11 gon the angles are all equal the measure of each is (11-2) times 180
then the result +x =180
again the same principal okay
do the same we did !! let me seee your work
so sum(11-2)180 is that how you substitute it
that's the sum of all angles is 11 gon
so the sum must be divided to 11 since they are all equal
so first you find the sum then divide by 11 ?
ok good, so how do you find the sum
i just showed (n-2)x180 is the sum of interior angles in any regular polygon no matter what is
here n=11 so (11-2)x180 is the total of all angles
Do you get what I'm saying?
kinda losing ya
okay! what is the sum of interior angles in a quadrilateral?
with four sides?
no i'm retriceing for the sum of all angles
im asking* (correction)
|dw:1435986516738:dw| sum of anlges in this
no that's the number of sides
i'm asking angles do you know what an angles is ?
wait is it 90 x 4
yes 90x4=360 but this does not work all the time only when the angles are 90 degree
not all shapes have the properties of that rectangle
the fact that i want you to draw into is any 4 sided gon have 360 as the total of all angles meaning if i measure all it angles one by one and sum them up i get 360 any 4 sided gon
we start with 3 sided (triangle) measure of all angles 180 4 sided gon: measure of all angles 360 5 sided gon measure of all angles 540 6 sided: 720 we follow this pattern... we get for any polygon with n sides: (n-2)x180 =============== so if we want the sum of all angles in 12 gon what we do is (12-2)x180=10x180=1800
9 gon (9-2)x180=7x180=1260 === 13 gon (13-2)x180=11x180=1980
do you get it now
so 11 x 180 ?
no don't you see what i'm doing
read again ho through you are not payng attention
11 gon (11-2)x180=9x180 11 take away 2 first then multiply by 180
ohhh now its starting to click
if it is what you did for 3 gon (triangle) you would have 3 times 180=540 which is false we know in a triangle angles sum up to 180
ok test fr you! what is the sum of angles in 14 gon
good! now i said that's the sum of all angle in a polygon for this problem we need the measure of each angle so we take that result and divide it by the number of sides
so in our case 11 gon 1620 is the result we divide it by 11
we should get 147.27 this is the measure of each angle in that shape you have
so thats the answer
now to get the exterior angle we know that angle on a straight line is 180 so what do we need to add to 147.27 to get 180
no not yet
we are looking for the exterior angle! not the interior
we found the interior so that we can find the exterior because we know that the exterior angle and the interior are supplementary meaning they add up to 180
if we know one we can get the other
hmm that's not satisfying answer! lol so all my talk is not enough lol
no its helping
you could also do 360/n to find an exterior angle measurement of a n-gon
a regular n-gon of course
yeah that's all permissible!
i'm using this method becausee it beneficial for non regular too for the asker
Oh I wasn't trying to put down your method or anything I was just giving another way to do it
oh no didn't feel down :) don't worry i like to see different ways
so 147.27+x=180 can you solve for x here @senpai_yerm
by the way we can use that as the formula to find a exterior angle of a regular n-gon because the sum of the exterior angles of any polygon is 360 deg and since we know a regular n-gon has the same exterior angles all the way around than we know each will have measure 360/n
here we need to round that nearest tenth
then u round up to 33 ?
!$#@&% yeaa thankyou
im just REALLYY slow at math
it's okay! as long as you understand
dam we spent almost an hour on this dam question... thanx for your patience