- anonymous

help again please

- chestercat

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- anonymous

##### 1 Attachment

- anonymous

this time its a 11-gon

- xapproachesinfinity

ok so 11 gon
the angles are all equal
the measure of each is (11-2) times 180

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## More answers

- xapproachesinfinity

then the result +x =180

- xapproachesinfinity

again the same principal okay

- anonymous

okay

- xapproachesinfinity

do the same we did !! let me seee your work

- anonymous

so sum(11-2)180 is that how you substitute it

- xapproachesinfinity

that's the sum of all angles is 11 gon

- xapproachesinfinity

so the sum must be divided to 11
since they are all equal

- anonymous

so first you find the sum then divide by 11 ?

- xapproachesinfinity

yes!

- anonymous

ok good, so how do you find the sum

- xapproachesinfinity

i just showed
(n-2)x180 is the sum of interior angles in any regular polygon no matter what is

- xapproachesinfinity

here n=11
so (11-2)x180 is the total of all angles

- xapproachesinfinity

Do you get what I'm saying?

- anonymous

kinda losing ya

- xapproachesinfinity

okay!
what is the sum of interior angles in a quadrilateral?

- xapproachesinfinity

with four sides?

- anonymous

4

- xapproachesinfinity

no i'm retriceing for the sum of all angles

- xapproachesinfinity

im asking* (correction)

- xapproachesinfinity

|dw:1435986516738:dw|
sum of anlges in this

- anonymous

4?

- xapproachesinfinity

no that's the number of sides

- xapproachesinfinity

i'm asking angles do you know what an angles is ?

- anonymous

wait is it 90 x 4

- xapproachesinfinity

yes 90x4=360
but this does not work all the time
only when the angles are 90 degree

- xapproachesinfinity

not all shapes have the properties of that rectangle

- xapproachesinfinity

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

- xapproachesinfinity

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

- xapproachesinfinity

9 gon
(9-2)x180=7x180=1260
===
13 gon
(13-2)x180=11x180=1980

- xapproachesinfinity

do you get it now

- anonymous

so 11 x 180 ?

- xapproachesinfinity

no don't you see what i'm doing

- xapproachesinfinity

read again ho through you are not payng attention

- xapproachesinfinity

11 gon
(11-2)x180=9x180
11 take away 2 first then multiply by 180

- anonymous

ohhh now its starting to click

- xapproachesinfinity

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

- xapproachesinfinity

ok test fr you!
what is the sum of angles in 14 gon

- anonymous

(14-2)x=180x12=2160 ???

- xapproachesinfinity

yes!

- xapproachesinfinity

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

- xapproachesinfinity

so in our case 11 gon
1620 is the result
we divide it by 11

- xapproachesinfinity

we should get 147.27
this is the measure of each angle in that shape you have

- anonymous

so thats the answer

- xapproachesinfinity

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

- xapproachesinfinity

no not yet

- xapproachesinfinity

we are looking for the exterior angle! not the interior

- xapproachesinfinity

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

- xapproachesinfinity

if we know one we can get the other

- xapproachesinfinity

get it?

- anonymous

starting to

- xapproachesinfinity

hmm that's not satisfying answer! lol
so all my talk is not enough lol

- anonymous

no its helping

- freckles

you could also do 360/n to find an exterior angle measurement of a n-gon

- freckles

a regular n-gon of course

- xapproachesinfinity

yeah that's all permissible!

- xapproachesinfinity

i'm using this method becausee it beneficial for non regular too for the asker

- freckles

Oh I wasn't trying to put down your method or anything
I was just giving another way to do it

- xapproachesinfinity

oh no didn't feel down :) don't worry
i like to see different ways

- xapproachesinfinity

so 147.27+x=180
can you solve for x here @senpai_yerm

- freckles

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

- xapproachesinfinity

true :)

- anonymous

32.73 ?

- xapproachesinfinity

yes!

- xapproachesinfinity

here we need to round that nearest tenth

- anonymous

then u round up to 33 ?

- xapproachesinfinity

yes!

- anonymous

!$#@&% yeaa thankyou

- xapproachesinfinity

np!

- anonymous

im just REALLYY slow at math

- xapproachesinfinity

it's okay! as long as you understand

- anonymous

dam we spent almost an hour on this dam question... thanx for your patience

- xapproachesinfinity

no problem!

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