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 3 years ago
If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?
 3 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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GT
 3 years ago
Best ResponseYou've already chosen the best response.0exterior angle? Can you draw which one it is?

moneybird
 3 years ago
Best ResponseYou've already chosen the best response.1n is the number of sides

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1To 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 \[n=360/24\] \[n=15\]

GT
 3 years ago
Best ResponseYou've already chosen the best response.0How is it then called exterior angle? That is the angle between two adjacent vertices and the center of the polygon.

moneybird
 3 years ago
Best ResponseYou've already chosen the best response.1i think exterior angle is 180  interior angle

moneybird
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1327116266165:dw

GT
 3 years ago
Best ResponseYou've already chosen the best response.0How can that be 24 for a polygon?

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1327116301791:dw Interior and exterior angles sum to 180

GT
 3 years ago
Best ResponseYou've already chosen the best response.0OK. 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.

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1Nope. 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: \[\sum=(n2)*180\] where n is the number of sides.

GT
 3 years ago
Best ResponseYou've already chosen the best response.0360/24 = 15. What is the issue there?

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1Sorry, that was a misread by me. :P

GT
 3 years ago
Best ResponseYou've already chosen the best response.0BTW  I hate that "formula" thing with n2 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.

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1I completely agree. It's just a much longer explanation for a forum like this.

GT
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah. But, I like calculating knowing geometric properties rather than having people memorize a formula.
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