# 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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by tarunsoni899

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by tarunsoni899

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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

**Number of sides = 2(1+a)**

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)