anonymous
  • anonymous
if each interior angle of a regular polygon measures 144 degrees, how many sides does the polygon have?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Please show steps on how to solve.
anonymous
  • anonymous
obtuse angles but idont know about a polygon with obtuse angles
JamesJ
  • JamesJ
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?

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More answers

anonymous
  • anonymous
the answer is supposed to be 10 sides how do you solve that?
anonymous
  • anonymous
decagon?
JamesJ
  • JamesJ
We'll get there ... follow me in logic first
anonymous
  • anonymous
ok
JamesJ
  • JamesJ
What's the sum of angles of a square?
anonymous
  • anonymous
180 (4-2) = 360
anonymous
  • anonymous
360 ofcourse.as all angles are 90
anonymous
  • anonymous
the polygon in question has 10 sides
anonymous
  • anonymous
^ why?
JamesJ
  • JamesJ
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.|dw:1327439866826:dw|
anonymous
  • anonymous
i know how to do that, how do you solve when you dont know the number of sides?
JamesJ
  • JamesJ
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 \[ \frac{180(n-2)}{n} \]
JamesJ
  • JamesJ
For your problem, set that equal to 144 and solve for n.
anonymous
  • anonymous
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
anonymous
  • anonymous
so, James J, i do 180 (n-2) / n = 144 144-180+2= n/n?
anonymous
  • anonymous
NOPE THATS NOT RIGHT ^
anonymous
  • anonymous
i dont understnad..
JamesJ
  • JamesJ
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?
anonymous
  • anonymous
OH WOW I GET IT!
anonymous
  • anonymous
sooo 180( n-2) = 144n wiat no, what do i do now?
JamesJ
  • JamesJ
...hence \[ 180n - 360 = 144n \] Now?
anonymous
  • anonymous
expand the brackets hellobudy
anonymous
  • anonymous
nope.. now what?
JamesJ
  • JamesJ
Subtract 144n from both sides... \[ 180n - 144n - 360 = 0 \] i.e. \[ 36n - 360 = 0 \] Now can you finish it?
anonymous
  • anonymous
-360 = -36 and then you divide 360 by 36 and you get ten
JamesJ
  • JamesJ
right, \[ 36n = 360 \] hence \[ n = \frac{360}{36} = 10 \]
anonymous
  • anonymous
k i think i get it..
anonymous
  • anonymous
thank you!
JamesJ
  • JamesJ
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.
anonymous
  • anonymous
ok! can you give me another example so i can practice? use a different degrees?
anonymous
  • anonymous
ok ill try with 100 degrees
JamesJ
  • JamesJ
No, that won't work. One sec.
JamesJ
  • JamesJ
try 108 degrees
anonymous
  • anonymous
ALRIGHT :)
anonymous
  • anonymous
5 sides?
JamesJ
  • JamesJ
yes
anonymous
  • anonymous
:D
JamesJ
  • JamesJ
last one, 162 degrees
anonymous
  • anonymous
20 :)
JamesJ
  • JamesJ
what about for 180 degrees?
anonymous
  • anonymous
huh?
JamesJ
  • JamesJ
That would correspond to a regular polygon with an infinite number of sides. What does that look like?
anonymous
  • anonymous
idk waht your asking
JamesJ
  • JamesJ
It would look like a circle.
JamesJ
  • JamesJ
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
anonymous
  • anonymous
thanks :)
anonymous
  • anonymous
g2g
JamesJ
  • JamesJ
Here's an even better picture of this idea:
1 Attachment
anonymous
  • anonymous
thanks!
anonymous
  • anonymous
Great job JamesJ - and way to hang in there hellobuddy!

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