Question

if each interior angle of a regular polygon measures 144 degrees, how many sides does the polygon have?

Answer 1

Please show steps on how to solve.

Answer 2

obtuse angles but idont know about a polygon with obtuse angles

Answer 3

Ok. What's the sum of angles of a triangle? 180 degrees. A triangle is a polygon with 3 sides.

What's the sum of the angles of a square? A square is a polygon with 4 sides. What's the answer here?

Answer 4

the answer is supposed to be 10 sides
how do you solve that?

Answer 5

decagon?

Answer 6

We'll get there ... follow me in logic first

Answer 7

ok

Answer 8

What's the sum of angles of a square?

Answer 9

180 (4-2) =
360

Answer 10

360 ofcourse.as all angles are 90

Answer 11

the polygon in question has 10 sides

Answer 12

^ why?

Answer 13

Right ... so you've got the formula for an n-sided polygon. It has a sum of angles
\[ 180(n-2) \]
and that's because you can make a polygon out of triangles. Stick two triangles together and you have a square, hence the sum of their angles is 180 + 180. Take a square add a triangle and you have a pentagon.

Answer 14

i know how to do that, how do you solve when you dont know the number of sides?

Answer 15

Now, if an n-sided polygon has a sum of angles 180(n-2), what's the size of the angles if each of them is the same? Well, there are n angles, hence one angle has the size of
\[ \frac{180(n-2)}{n} \]

Answer 16

For your problem, set that equal to 144 and solve for n.

Answer 17

the general rule is
Each Angle (of a Regular Polygon) = (n-2) × 180° / n
so 144=(n-2)x180/n
144n=(n-2)x180
144n=180n-360
144n-180n=-360
36n=360
n=10

Answer 18

so, James J, i do 180 (n-2) / n = 144
144-180+2= n/n?

Answer 19

NOPE THATS NOT RIGHT ^

Answer 20

i dont understnad..

Answer 21

Safiah has written this out for you. But to start it off again
\[ \frac{180(n-2)}{n} = 144 \]
hence
\[ 180(n-2) = 144n \]
Can you do it now?

Answer 22

OH WOW
I GET IT!

Answer 23

sooo 180( n-2) = 144n
wiat no, what do i do now?

Answer 24

...hence
\[ 180n - 360 = 144n \]
Now?

Answer 25

expand the brackets hellobudy

Answer 26

nope.. now what?

Answer 27

Subtract 144n from both sides...
\[ 180n - 144n - 360 = 0 \]
i.e.
\[ 36n - 360 = 0 \]
Now can you finish it?

Answer 28

-360 = -36
and then you divide 360 by 36
and you get ten

Answer 29

right,
\[ 36n = 360 \]
hence
\[ n = \frac{360}{36} = 10 \]

Answer 30

k i think i get it..

Answer 31

thank you!

Answer 32

Do yourself a favor. Take a blank piece of paper. Write out the solution again. When you can do that without looking at anything --such as this web or another version of the solution--then you know you understand the solution.

Answer 33

ok! can you give me another example so i can practice? use a different degrees?

Answer 34

ok ill try with 100 degrees

Answer 35

No, that won't work. One sec.

Answer 36

try 108 degrees

Answer 37

ALRIGHT :)

Answer 38

5 sides?

Answer 39

yes

Answer 40

:D

Answer 41

last one, 162 degrees

Answer 42

20 :)

Answer 43

what about for 180 degrees?

Answer 44

huh?

Answer 45

That would correspond to a regular polygon with an infinite number of sides. What does that look like?

Answer 46

idk waht your asking

Answer 47

It would look like a circle.

Answer 48

As you add more and more sides to a regular polygon, it looks more and more like a circle. In the limit, as the number of sides goes to infinity, it would become a circle.
http://www.ck12.org/ck12/images?id=301055

Answer 49

thanks :)

Answer 50

g2g

Answer 51

Here's an even better picture of this idea:

Answer 52

thanks!

Answer 53

Great job JamesJ - and way to hang in there hellobuddy!