A polygon has n sides. An interior angle of the polygon and an adjacent
exterior angle form a straight angle.
a. What is the sum of the measures of the n straight angles?
b. What is the sum of the measures of the n interior angles?
c. Using your answers above, what is the sum of the measures of the n exterior
angles?
d. What theorem do the steps above prove?

- highschoolmom2010

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- highschoolmom2010

A i think is 180

- ganeshie8

thats right, ONE straight angle makes 180

- ganeshie8

so, 'n' straight angles make '180n' angle

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## More answers

- ganeshie8

is that clear ha

- highschoolmom2010

c is 360

- ganeshie8

lets take one thing at a time :)

- highschoolmom2010

and i thing that d is a regular polygon

- highschoolmom2010

:) so in dont forget

- ganeshie8

you're right mostly :) lets do these one by one okay :D

- ganeshie8

a) sum of n straight angles = 180n

- ganeshie8

b. What is the sum of the measures of the n interior angles?
you have any ideas for this ?

- highschoolmom2010

is it 180

- ganeshie8

nope, sum of measures of n interior angles = 180(n-2)

- ganeshie8

remember that formula ha ?

- highschoolmom2010

oh i did nt know you were wanting the formula

- ganeshie8

question asks about formula oly cuz it asks for "n" anlges. it doesnt say whats n

- highschoolmom2010

yea i know about (n-2)180

- ganeshie8

good :) then move on to c (i can explain how it is (n-2)180... but its not required to knw for this problem )

- highschoolmom2010

360

- ganeshie8

how u got 360

- ganeshie8

c. Using your answers above, what is the sum of the measures of the n exterior
angles?

- ganeshie8

it wants you to use a, b answers to get 360

- highschoolmom2010

wait i mis read that

- ganeshie8

no, you have read it correctly. oly thing missing is, you need to use a, b to prove sum of exterior angels equals 360

- ganeshie8

u shouldnt simply say its 360, you need to prove it

- highschoolmom2010

how do i do that

- ganeshie8

il show the complete solution, see if u can understand it

- ganeshie8

its simple and short, so nothing to wry ok :)

- highschoolmom2010

ok

- ganeshie8

From a, we have :-
sum of n straight angles = 180n

- ganeshie8

but, it is given that "interior angle + exterior angle = 180"

- ganeshie8

so,
sum of exterior angles + sum of interior angles = 180n

- highschoolmom2010

ok

- ganeshie8

sum of exterior angels + 180(n-2) = 180n

- ganeshie8

sum of exterior angels = 180n - 180(n-2)

- ganeshie8

simplify

- ganeshie8

no dont do that

- ganeshie8

sum of exterior angels = 180n - 180(n-2)
= 180n - 180n + 360
= 360

- ganeshie8

hope u see lol

- highschoolmom2010

oh yea ok i see

- ganeshie8

:) takes time im sure

- highschoolmom2010

yea it was confusing

- ganeshie8

first time its confusing

- ganeshie8

go thru again and again, just dont give up cuz its worth the time...

- highschoolmom2010

and if i keep having issues ill keep asking you lol

- ganeshie8

sure il be happy to assist a brilliant student like u :)

- highschoolmom2010

was i right about it being a regular polygon

- ganeshie8

what we proved ?

- ganeshie8

we have proven that "sum of exterior angles = 360"

- highschoolmom2010

letter D. yes

- ganeshie8

its called "Polygon Exterior Angle Sum Theorem"

- ganeshie8

so we have proven that theorem :)

- highschoolmom2010

oh ok but is it a regular polygon

- ganeshie8

it works for ANY polygon

- ganeshie8

irregular or regular - it doesnt matter

- ganeshie8

|dw:1371136729910:dw|

- highschoolmom2010

oh okay

- ganeshie8

how many degrees a circle has ?

- highschoolmom2010

360

- ganeshie8

|dw:1371136782890:dw|

- ganeshie8

if u start from the start, it takes 360 degrees to come back to start position

- ganeshie8

in any polygon, the same thing happens.

- highschoolmom2010

oh okay

- ganeshie8

when ever u bend, you always bend some oly. by the time u get back to start, u would have bent 360. i knw these make no sense to u lol

- ganeshie8

|dw:1371136923648:dw|

- ganeshie8

just gimme 2 mnts, il try to explain, u try to pay attention... see if we can work these out ok

- ganeshie8

imagine, you standing at that black dot.

- highschoolmom2010

alright im at the black dot

- ganeshie8

walk right a bit

- ganeshie8

|dw:1371137103674:dw|

- ganeshie8

when u hit that corner, stop.

- ganeshie8

you need to take a bend, cuz u want to walk along that pentagon.

- ganeshie8

|dw:1371137191206:dw|

- ganeshie8

thats ur first bend

- ganeshie8

now tell me this, how many times u need to bend, before u come back to where u started ?

- highschoolmom2010

4

- ganeshie8

almost right, but its 5 times actually. u missed the last bend.

- highschoolmom2010

well you go around 5 lines

- ganeshie8

so you complete a full circle when u go along a polygon

- ganeshie8

|dw:1371137372193:dw|

- ganeshie8

a full circle is always 360. it DOESNT matter how many times u bend. u have to bend a full 360 to come back.

- ganeshie8

if the polygon has more sides, u wil be bending more times. but each time u wil bending oly a little

- highschoolmom2010

alright

- ganeshie8

if the polygon has few sides, u wil be bending oly few times. but each time u wil be bending a more angle.

- ganeshie8

its okay if u dont get it, i can understand... move on :)

- highschoolmom2010

i am slowly understanding

- ganeshie8

good :)

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