Question

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

Answer 1

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)

Answer 2

In terms of a, number of sides = 2(1+a)=2a+2