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rational
 one year ago
show that if three angles in a convex polygon are equal to \(60^{\circ}\) then it must be an equilateral triangle
rational
 one year ago
show that if three angles in a convex polygon are equal to \(60^{\circ}\) then it must be an equilateral triangle

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ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2dw:1439061574644:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2i'll try other form dw:1439061670041:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2assume x is 60 dw:1439061819528:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2(if it works for quadrilateral then it works for any polygon ) geometric logic so we need to show by contradiction that we cant construct a quadrilateral with 3 60 angle

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2that would make the other angle 180 seems more like not concave nor convex

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2dw:1439062235117:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2i feel sleepy i might write it more need in morning,gn

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sum of all the exterior angles of a polygon is 360 degrees. The exterior angle corresponding to 60 degrees is 120 degrees. Since three angles are 60 degrees, the sum of those exterior angles is 120*3 = 360 degrees. Thus there can be no other nonzero exterior angle corresponding to a vertex. So, these are the only 3 vertices, and the polygon is an equilateral triangle.

rational
 one year ago
Best ResponseYou've already chosen the best response.1Nice :) More generally : Any convex polygon with \(n\) angles equal to \(\dfrac{360}{n}\) must be a regular \(\text{ngon}\)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2hehehe ok that was direct

rational
 one year ago
Best ResponseYou've already chosen the best response.1* Any convex polygon with \(n\) angles equal to \(180\dfrac{360}{n}\) must be a regular \(\text{ngon}\)

rational
 one year ago
Best ResponseYou've already chosen the best response.1for example, in a square we have \(4\) angles equal to \(180\frac{360}{4} = 90\)
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