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hellobuddy Group Title

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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  1. hellobuddy Group Title
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    Please show steps on how to solve.

    • 2 years ago
  2. jesusisrisen Group Title
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    obtuse angles but idont know about a polygon with obtuse angles

    • 2 years ago
  3. JamesJ Group Title
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    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
  4. hellobuddy Group Title
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    the answer is supposed to be 10 sides how do you solve that?

    • 2 years ago
  5. jesusisrisen Group Title
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    decagon?

    • 2 years ago
  6. JamesJ Group Title
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    We'll get there ... follow me in logic first

    • 2 years ago
  7. hellobuddy Group Title
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    ok

    • 2 years ago
  8. JamesJ Group Title
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    What's the sum of angles of a square?

    • 2 years ago
  9. hellobuddy Group Title
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    180 (4-2) = 360

    • 2 years ago
  10. Safiah Group Title
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    360 ofcourse.as all angles are 90

    • 2 years ago
  11. Safiah Group Title
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    the polygon in question has 10 sides

    • 2 years ago
  12. hellobuddy Group Title
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    ^ why?

    • 2 years ago
  13. JamesJ Group Title
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    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|

    • 2 years ago
  14. hellobuddy Group Title
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    i know how to do that, how do you solve when you dont know the number of sides?

    • 2 years ago
  15. JamesJ Group Title
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    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 \[ \frac{180(n-2)}{n} \]

    • 2 years ago
  16. JamesJ Group Title
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    For your problem, set that equal to 144 and solve for n.

    • 2 years ago
  17. Safiah Group Title
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    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

    • 2 years ago
  18. hellobuddy Group Title
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    so, James J, i do 180 (n-2) / n = 144 144-180+2= n/n?

    • 2 years ago
  19. hellobuddy Group Title
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    NOPE THATS NOT RIGHT ^

    • 2 years ago
  20. hellobuddy Group Title
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    i dont understnad..

    • 2 years ago
  21. JamesJ Group Title
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    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?

    • 2 years ago
  22. hellobuddy Group Title
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    OH WOW I GET IT!

    • 2 years ago
  23. hellobuddy Group Title
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    sooo 180( n-2) = 144n wiat no, what do i do now?

    • 2 years ago
  24. JamesJ Group Title
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    ...hence \[ 180n - 360 = 144n \] Now?

    • 2 years ago
  25. Safiah Group Title
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    expand the brackets hellobudy

    • 2 years ago
  26. hellobuddy Group Title
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    nope.. now what?

    • 2 years ago
  27. JamesJ Group Title
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    Subtract 144n from both sides... \[ 180n - 144n - 360 = 0 \] i.e. \[ 36n - 360 = 0 \] Now can you finish it?

    • 2 years ago
  28. hellobuddy Group Title
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    -360 = -36 and then you divide 360 by 36 and you get ten

    • 2 years ago
  29. JamesJ Group Title
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    right, \[ 36n = 360 \] hence \[ n = \frac{360}{36} = 10 \]

    • 2 years ago
  30. hellobuddy Group Title
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    k i think i get it..

    • 2 years ago
  31. hellobuddy Group Title
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    thank you!

    • 2 years ago
  32. JamesJ Group Title
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    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.

    • 2 years ago
  33. hellobuddy Group Title
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    ok! can you give me another example so i can practice? use a different degrees?

    • 2 years ago
  34. hellobuddy Group Title
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    ok ill try with 100 degrees

    • 2 years ago
  35. JamesJ Group Title
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    No, that won't work. One sec.

    • 2 years ago
  36. JamesJ Group Title
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    try 108 degrees

    • 2 years ago
  37. hellobuddy Group Title
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    ALRIGHT :)

    • 2 years ago
  38. hellobuddy Group Title
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    5 sides?

    • 2 years ago
  39. JamesJ Group Title
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    yes

    • 2 years ago
  40. hellobuddy Group Title
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    :D

    • 2 years ago
  41. JamesJ Group Title
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    last one, 162 degrees

    • 2 years ago
  42. hellobuddy Group Title
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    20 :)

    • 2 years ago
  43. JamesJ Group Title
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    what about for 180 degrees?

    • 2 years ago
  44. hellobuddy Group Title
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    huh?

    • 2 years ago
  45. JamesJ Group Title
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    That would correspond to a regular polygon with an infinite number of sides. What does that look like?

    • 2 years ago
  46. hellobuddy Group Title
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    idk waht your asking

    • 2 years ago
  47. JamesJ Group Title
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    It would look like a circle.

    • 2 years ago
  48. JamesJ Group Title
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    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
  49. hellobuddy Group Title
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    thanks :)

    • 2 years ago
  50. hellobuddy Group Title
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    g2g

    • 2 years ago
  51. JamesJ Group Title
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    Here's an even better picture of this idea:

    • 2 years ago
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  52. hellobuddy Group Title
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    thanks!

    • 2 years ago
  53. cshalvey Group Title
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    Great job JamesJ - and way to hang in there hellobuddy!

    • 2 years ago
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