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

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

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