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The result of dividing the interior angles of a regular polygon by its exterior angle is 2.5, find the number of sides of the polygon​

 Feb 21, 2021
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Let   the  exterior  angle  = x

Let the interior  angle =  2.5x 

 

So....the  sum of  an interior angle and its  exterior angle  = 180°

 

So.......

 

x  +  2.5x     =  180

3.5x  = 180

x = 180  / 3.5  = 360/7   =  the  exterior  angle

 

Since  the  sum  of the exterior angles of a polygon  =  360   the polygon must have  7  sides

 

 

cool cool cool

 Feb 21, 2021

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