anonymous
  • anonymous
If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
exterior angle? Can you draw which one it is?
anonymous
  • anonymous
360/n = 24
anonymous
  • anonymous
n is the number of sides

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anonymous
  • anonymous
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 \[n=360/24\] \[n=15\]
anonymous
  • anonymous
How is it then called exterior angle? That is the angle between two adjacent vertices and the center of the polygon.
anonymous
  • anonymous
i think exterior angle is 180 - interior angle
anonymous
  • anonymous
|dw:1327116266165:dw|
anonymous
  • anonymous
How can that be 24 for a polygon?
anonymous
  • anonymous
|dw:1327116301791:dw| Interior and exterior angles sum to 180
anonymous
  • anonymous
It's 24 sides
anonymous
  • anonymous
See that drawing helped.
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
360/24 = 15. What is the issue there?
anonymous
  • anonymous
Sorry, that was a misread by me. :-P
anonymous
  • anonymous
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.
anonymous
  • anonymous
I completely agree. It's just a much longer explanation for a forum like this.
anonymous
  • anonymous
Yeah. But, I like calculating knowing geometric properties rather than having people memorize a formula.

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