Question

Ugh, more Geometry. .-.
Help with confusing question, please?
Thanks!!
(ﾉ^ヮ^)ﾉ*:・ﾟ✧*:・ﾟ✧

Answer 1

The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex.
How many sides does the polygon have?

Answer 2

we will use s for interior and o for exterior since \(\it i\) and \(\it e\) are something completely different

Answer 3

The sum of the interior angles of any polygon is \[180(n -2)\]where n is the # of sides.
The sum sum of the exterior angles of any polygon is 360 degrees.

Answer 4

exterior angles must equal 360 so we know that o=360
s=5(360)

Answer 5

s=1800

Answer 6

that is the sum of the interior angles so now we must find the number of sides

Answer 7

@sleepyjess teach, don't just give the answers. You're really not helping if you're just giving the answers.

Answer 8

Ehh, I don't see where any answers were given @calculusfunctions
But okay.. the formula is 180(n-2)
Then what? (Meaning what is the next step?)

Answer 9

I know we have to do some form of algebra next, but how do I set it up?

Answer 10

you know that the sum is 1800
so you would do 1800=180(n-2) then solve for n
do you know how to start that?

Answer 11

You would divide by 180, right?

Answer 12

Yes, because you are multiplying on the right side, you would divide both sides to get rid of 180.

Answer 13

so what is 1800/180?

Answer 14

I got 10

Answer 15

correct so now what is your equation?

Answer 16

10(n-2), right?

Answer 17

almost
you would have 10=n-2
remember you got rid of 180 on the right side

Answer 18

Ohh okay.
So now we get rid of the n?

Answer 19

nope now we get rid of the -2
how do you think you would do that?

Answer 20

Add to both sides?

Answer 21

yes
so now we have 10+2=n-2+2
which is equal to 12=n

Answer 22

to confirm that you can substitute 12 for n and see if it equals 1800

Answer 23

180(12-2)
180(10)
1800

Answer 24

Ohhhh, okay, that makes sense now!!
\(\Large\frak\color{blueviolet}{Thanks!}\)

Answer 25

\(\Large\frak\color{blueviolet}{No~problem!}\)

Answer 26

so our shape has 12 sides \(\Huge\ddot\smile\ddot\smile\ddot\smile\ddot\smile\ddot\smile\ddot\smile\ddot\smile\ddot\smile\ddot\smile\ddot\smile\\\Huge\ddot\smile\ddot\smile\ddot\smile\ddot\smile\)

Answer 27

\(\Large\frak\color{magenta}{YAYYYY!!!!}\)
XD

Answer 28

\(\Huge\cal\color{purple}{Don't~worry,\\you~and~I~both~feel~the\\same~way,~you~about\\geometry,~me~about\\pre-calc.}\)