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Each interior angle of regular polygon is 'a' times of its exterior angle. Find , in terms of a, the number of sides in the polygon




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In a polygon, 
interior angle + exterior angle = 180

if the interior angle is a times the exterior angle,
exterior angle = x
interior angle = ax
sum = x + ax = 180
⇒x(1+a) = 180
⇒ x = 180/(1+a)

Also the sum of exterior angles is 360.
If a polygon has n sides, it will have n exterior angles

n*x=360 \\  \\ n= \frac{360}{x}  \\  \\ n= \frac{360}{( \frac{180}{1+a} )} = \frac{360*(1+a)}{180} =2(1+a)

Number of sides = 2(1+a)

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if a regular polygon has n sides, then sum of internal angles is 180(n-2)
but sum of exterior angles remain 360.
i know all these things thanks for your concern !!!!
enjoy ur time !!! :)
In terms of a, number of sides = 2(1+a)=2a+2
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