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

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hellobuddyBest ResponseYou've already chosen the best response.0
Please show steps on how to solve.
 2 years ago

jesusisrisenBest ResponseYou've already chosen the best response.0
obtuse angles but idont know about a polygon with obtuse angles
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
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?
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
the answer is supposed to be 10 sides how do you solve that?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
We'll get there ... follow me in logic first
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
What's the sum of angles of a square?
 2 years ago

SafiahBest ResponseYou've already chosen the best response.2
360 ofcourse.as all angles are 90
 2 years ago

SafiahBest ResponseYou've already chosen the best response.2
the polygon in question has 10 sides
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
Right ... so you've got the formula for an nsided polygon. It has a sum of angles \[ 180(n2) \] 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
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
i know how to do that, how do you solve when you dont know the number of sides?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
Now, if an nsided polygon has a sum of angles 180(n2), 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 \[ \frac{180(n2)}{n} \]
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
For your problem, set that equal to 144 and solve for n.
 2 years ago

SafiahBest ResponseYou've already chosen the best response.2
the general rule is Each Angle (of a Regular Polygon) = (n2) × 180° / n so 144=(n2)x180/n 144n=(n2)x180 144n=180n360 144n180n=360 36n=360 n=10
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
so, James J, i do 180 (n2) / n = 144 144180+2= n/n?
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
NOPE THATS NOT RIGHT ^
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
Safiah has written this out for you. But to start it off again \[ \frac{180(n2)}{n} = 144 \] hence \[ 180(n2) = 144n \] Can you do it now?
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
sooo 180( n2) = 144n wiat no, what do i do now?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
...hence \[ 180n  360 = 144n \] Now?
 2 years ago

SafiahBest ResponseYou've already chosen the best response.2
expand the brackets hellobudy
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
Subtract 144n from both sides... \[ 180n  144n  360 = 0 \] i.e. \[ 36n  360 = 0 \] Now can you finish it?
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
360 = 36 and then you divide 360 by 36 and you get ten
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
right, \[ 36n = 360 \] hence \[ n = \frac{360}{36} = 10 \]
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
k i think i get it..
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
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 solutionthen you know you understand the solution.
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
ok! can you give me another example so i can practice? use a different degrees?
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
ok ill try with 100 degrees
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
No, that won't work. One sec.
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
what about for 180 degrees?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
That would correspond to a regular polygon with an infinite number of sides. What does that look like?
 2 years ago

hellobuddyBest ResponseYou've already chosen the best response.0
idk waht your asking
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
It would look like a circle.
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
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
 2 years ago

JamesJBest ResponseYou've already chosen the best response.7
Here's an even better picture of this idea:
 2 years ago

cshalveyBest ResponseYou've already chosen the best response.0
Great job JamesJ  and way to hang in there hellobuddy!
 2 years ago
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