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Question

If the interior angle of a regular polygon is double the exterior angle then the polygon is ___


  1. Triangle

  2. Pentagon

  3. Hexagon

  4. Octagon


Solution

The correct option is C

Hexagon


 It is given that the polygon is regular. So all the sides and angles of the polygon are equal.

Let exterior angle = e°    Interior angle = 2e° 

In a polygon, the sum of an interior angle and its respective exterior angle is 180°

 interior angle +  exterior angle = 180°

2e + e = 180°

 3e = 180°

e = 60°

exterior angle = 60°

Sum of exterior angles of any polygon = 360

n × exterior angle = 360  (where, n= Number of sides)

n =360°exterior angle 

        = 360°60°

        = 6

Number of sides of polygon is 6, so the given polygon is hexagon.

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