Question

A polygon has n sides. Two of its angles are right angles. Each of the remaining angles equal to 150 degrees. calculate n. Please help! =)

Answer 1

Two of its angles are right angles...so we have 2*90 = 180 degrees so far

Answer 2

The remaining angles are 150 degrees

there are n-2 angles left since we used up 2 angles (above), so the remaining angles add up to

150(n-2)

Answer 3

in total, all n angles add to

180 + 150(n-2)

Answer 4

now, you can use the formula

S = 180(n-2)

to find the sum of the interior angles of any polygon with n sides

Answer 5

so if all angles add to 180 + 150(n-2)

AND

they add to 180(n-2)

then

180(n-2) = 180 + 150(n-2)

Answer 6

solve for n

Answer 7

the answer would be 8 right because i found this online: For a polygon of n sides, the sum of all angles is 180n – 360 degrees

We are given that two sides are 90 degrees and the remainder are 150 degrees

Therefore 180n – 360 = 150(n – 2) + 90 x 2 = 150n – 300 + 180



180n = 150n + 360 + 180 – 300

30n = 240

n = 8

Therefore it is an octagon with six angles 150 degrees and two right angles

Answer 8

that is correct

Answer 9

solving 180(n-2) = 180 + 150(n-2) for n gives you n = 8

Answer 10

but i am not understanding that procedure =/

Answer 11

which one: mine or the thing you found online?

Answer 12

both =/

Answer 13

ok where are you stuck on mine?

Answer 14

how did you get the answer 8

Answer 15

do you know how to solve 180(n-2) = 180 + 150(n-2) for n?

Answer 16

nope =/

Answer 17

ok first distribute

180(n-2) = 180 + 150(n-2)

180n-360 = 180 + 150n-300

what's next?

Answer 18

where did the 300 come from =/

Answer 19

150 times 2 = 300

Answer 20

150 times -2 = -300

Answer 21

ohh

Answer 22

so what's next?

Answer 23

you would have to group the numbers =/

Answer 24

180 - 300 = ???

Answer 25

-120

Answer 26

so

180n-360 = 180 + 150n-300

turns into

180n-360 = 150n-120

Answer 27

then what?

Answer 28

dont you group them like:
180n-150n=-120+360

Answer 29

very good

Answer 30

basically you get the like terms to the same side

Answer 31

180n - 150n = ???

Answer 32

30n

Answer 33

good

Answer 34

-120 + 360 = ?

Answer 35

then the other answer is 240

Answer 36

so we can say

30n = 240

Answer 37

then you divide 240 by 30

Answer 38

which in english translates to

30 times some number equals 240

Answer 39

perfect

Answer 40

Thank you very much! Finally i understand!

Answer 41

ok that's great that you do