Question

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?

Answer 1

A i think is 180

Answer 2

thats right, ONE straight angle makes 180

Answer 3

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

Answer 4

is that clear ha

Answer 5

c is 360

Answer 6

lets take one thing at a time :)

Answer 7

and i thing that d is a regular polygon

Answer 8

:) so in dont forget

Answer 9

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

Answer 10

a) sum of n straight angles = 180n

Answer 11

b. What is the sum of the measures of the n interior angles?

you have any ideas for this ?

Answer 12

is it 180

Answer 13

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

Answer 14

remember that formula ha ?

Answer 15

oh i did nt know you were wanting the formula

Answer 16

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

Answer 17

yea i know about (n-2)180

Answer 18

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

Answer 19

360

Answer 20

how u got 360

Answer 21

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

Answer 22

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

Answer 23

wait i mis read that

Answer 24

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

Answer 25

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

Answer 26

how do i do that

Answer 27

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

Answer 28

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

Answer 29

ok

Answer 30

From a, we have :-

sum of n straight angles = 180n

Answer 31

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

Answer 32

so,

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

Answer 33

ok

Answer 34

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

Answer 35

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

Answer 36

simplify

Answer 37

no dont do that

Answer 38

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

Answer 39

hope u see lol

Answer 40

oh yea ok i see

Answer 41

:) takes time im sure

Answer 42

yea it was confusing

Answer 43

first time its confusing

Answer 44

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

Answer 45

and if i keep having issues ill keep asking you lol

Answer 46

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

Answer 47

was i right about it being a regular polygon

Answer 48

what we proved ?

Answer 49

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

Answer 50

letter D. yes

Answer 51

its called "Polygon Exterior Angle Sum Theorem"

Answer 52

so we have proven that theorem :)

Answer 53

oh ok but is it a regular polygon

Answer 54

it works for ANY polygon

Answer 55

irregular or regular - it doesnt matter

Answer 56

oh okay

Answer 57

how many degrees a circle has ?

Answer 58

360