highschoolmom2010
  • highschoolmom2010
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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highschoolmom2010
  • highschoolmom2010
A i think is 180
ganeshie8
  • ganeshie8
thats right, ONE straight angle makes 180
ganeshie8
  • ganeshie8
so, 'n' straight angles make '180n' angle

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More answers

ganeshie8
  • ganeshie8
is that clear ha
highschoolmom2010
  • highschoolmom2010
c is 360
ganeshie8
  • ganeshie8
lets take one thing at a time :)
highschoolmom2010
  • highschoolmom2010
and i thing that d is a regular polygon
highschoolmom2010
  • highschoolmom2010
:) so in dont forget
ganeshie8
  • ganeshie8
you're right mostly :) lets do these one by one okay :D
ganeshie8
  • ganeshie8
a) sum of n straight angles = 180n
ganeshie8
  • ganeshie8
b. What is the sum of the measures of the n interior angles? you have any ideas for this ?
highschoolmom2010
  • highschoolmom2010
is it 180
ganeshie8
  • ganeshie8
nope, sum of measures of n interior angles = 180(n-2)
ganeshie8
  • ganeshie8
remember that formula ha ?
highschoolmom2010
  • highschoolmom2010
oh i did nt know you were wanting the formula
ganeshie8
  • ganeshie8
question asks about formula oly cuz it asks for "n" anlges. it doesnt say whats n
highschoolmom2010
  • highschoolmom2010
yea i know about (n-2)180
ganeshie8
  • 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
  • highschoolmom2010
360
ganeshie8
  • ganeshie8
how u got 360
ganeshie8
  • ganeshie8
c. Using your answers above, what is the sum of the measures of the n exterior angles?
ganeshie8
  • ganeshie8
it wants you to use a, b answers to get 360
highschoolmom2010
  • highschoolmom2010
wait i mis read that
ganeshie8
  • 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
  • ganeshie8
u shouldnt simply say its 360, you need to prove it
highschoolmom2010
  • highschoolmom2010
how do i do that
ganeshie8
  • ganeshie8
il show the complete solution, see if u can understand it
ganeshie8
  • ganeshie8
its simple and short, so nothing to wry ok :)
highschoolmom2010
  • highschoolmom2010
ok
ganeshie8
  • ganeshie8
From a, we have :- sum of n straight angles = 180n
ganeshie8
  • ganeshie8
but, it is given that "interior angle + exterior angle = 180"
ganeshie8
  • ganeshie8
so, sum of exterior angles + sum of interior angles = 180n
highschoolmom2010
  • highschoolmom2010
ok
ganeshie8
  • ganeshie8
sum of exterior angels + 180(n-2) = 180n
ganeshie8
  • ganeshie8
sum of exterior angels = 180n - 180(n-2)
ganeshie8
  • ganeshie8
simplify
ganeshie8
  • ganeshie8
no dont do that
ganeshie8
  • ganeshie8
sum of exterior angels = 180n - 180(n-2) = 180n - 180n + 360 = 360
ganeshie8
  • ganeshie8
hope u see lol
highschoolmom2010
  • highschoolmom2010
oh yea ok i see
ganeshie8
  • ganeshie8
:) takes time im sure
highschoolmom2010
  • highschoolmom2010
yea it was confusing
ganeshie8
  • ganeshie8
first time its confusing
ganeshie8
  • ganeshie8
go thru again and again, just dont give up cuz its worth the time...
highschoolmom2010
  • highschoolmom2010
and if i keep having issues ill keep asking you lol
ganeshie8
  • ganeshie8
sure il be happy to assist a brilliant student like u :)
highschoolmom2010
  • highschoolmom2010
was i right about it being a regular polygon
ganeshie8
  • ganeshie8
what we proved ?
ganeshie8
  • ganeshie8
we have proven that "sum of exterior angles = 360"
highschoolmom2010
  • highschoolmom2010
letter D. yes
ganeshie8
  • ganeshie8
its called "Polygon Exterior Angle Sum Theorem"
ganeshie8
  • ganeshie8
so we have proven that theorem :)
highschoolmom2010
  • highschoolmom2010
oh ok but is it a regular polygon
ganeshie8
  • ganeshie8
it works for ANY polygon
ganeshie8
  • ganeshie8
irregular or regular - it doesnt matter
ganeshie8
  • ganeshie8
|dw:1371136729910:dw|
highschoolmom2010
  • highschoolmom2010
oh okay
ganeshie8
  • ganeshie8
how many degrees a circle has ?
highschoolmom2010
  • highschoolmom2010
360
ganeshie8
  • ganeshie8
|dw:1371136782890:dw|
ganeshie8
  • ganeshie8
if u start from the start, it takes 360 degrees to come back to start position
ganeshie8
  • ganeshie8
in any polygon, the same thing happens.
highschoolmom2010
  • highschoolmom2010
oh okay
ganeshie8
  • 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
  • ganeshie8
|dw:1371136923648:dw|
ganeshie8
  • ganeshie8
just gimme 2 mnts, il try to explain, u try to pay attention... see if we can work these out ok
ganeshie8
  • ganeshie8
imagine, you standing at that black dot.
highschoolmom2010
  • highschoolmom2010
alright im at the black dot
ganeshie8
  • ganeshie8
walk right a bit
ganeshie8
  • ganeshie8
|dw:1371137103674:dw|
ganeshie8
  • ganeshie8
when u hit that corner, stop.
ganeshie8
  • ganeshie8
you need to take a bend, cuz u want to walk along that pentagon.
ganeshie8
  • ganeshie8
|dw:1371137191206:dw|
ganeshie8
  • ganeshie8
thats ur first bend
ganeshie8
  • ganeshie8
now tell me this, how many times u need to bend, before u come back to where u started ?
highschoolmom2010
  • highschoolmom2010
4
ganeshie8
  • ganeshie8
almost right, but its 5 times actually. u missed the last bend.
highschoolmom2010
  • highschoolmom2010
well you go around 5 lines
ganeshie8
  • ganeshie8
so you complete a full circle when u go along a polygon
ganeshie8
  • ganeshie8
|dw:1371137372193:dw|
ganeshie8
  • 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
  • ganeshie8
if the polygon has more sides, u wil be bending more times. but each time u wil bending oly a little
highschoolmom2010
  • highschoolmom2010
alright
ganeshie8
  • 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
  • ganeshie8
its okay if u dont get it, i can understand... move on :)
highschoolmom2010
  • highschoolmom2010
i am slowly understanding
ganeshie8
  • ganeshie8
good :)

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