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kamuela710

  • 2 years ago

If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?

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  1. GT
    • 2 years ago
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    exterior angle? Can you draw which one it is?

  2. moneybird
    • 2 years ago
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    360/n = 24

  3. moneybird
    • 2 years ago
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    n is the number of sides

  4. MrYantho
    • 2 years ago
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    To do this, we have to remember two things: 1. The exterior angles of a polygon ALWAYS add up to 360 degress 2. A regular polygon's angles are all equal (including exterior) So, every exterior angle is 24 \[n=360/24\] \[n=15\]

  5. GT
    • 2 years ago
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    How is it then called exterior angle? That is the angle between two adjacent vertices and the center of the polygon.

  6. moneybird
    • 2 years ago
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    i think exterior angle is 180 - interior angle

  7. moneybird
    • 2 years ago
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    |dw:1327116266165:dw|

  8. GT
    • 2 years ago
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    How can that be 24 for a polygon?

  9. MrYantho
    • 2 years ago
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    |dw:1327116301791:dw| Interior and exterior angles sum to 180

  10. moneybird
    • 2 years ago
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    It's 24 sides

  11. GT
    • 2 years ago
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    See that drawing helped.

  12. GT
    • 2 years ago
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    OK. Then, the interior angle is 156. So, the angle at the center of the polygon must be 24 also. Therefore, 360/24 sides. Got it.

  13. MrYantho
    • 2 years ago
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    Nope. There are 15 sides (see earlier answer). Exterior angles always sum to 360 no matter how many sides. So it is n=360/24 The sum of interior angles is different depending on the number of sides: \[\sum=(n-2)*180\] where n is the number of sides.

  14. GT
    • 2 years ago
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    360/24 = 15. What is the issue there?

  15. MrYantho
    • 2 years ago
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    Sorry, that was a misread by me. :-P

  16. GT
    • 2 years ago
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    BTW - I hate that "formula" thing with n-2 thing. It is unnecessary. Basic triangle property of angles and the circle being 360 degrees does the trick here, and then it is all basic arithmetic.

  17. MrYantho
    • 2 years ago
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    I completely agree. It's just a much longer explanation for a forum like this.

  18. GT
    • 2 years ago
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    Yeah. But, I like calculating knowing geometric properties rather than having people memorize a formula.

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