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Question

If the ratio of the exterior angle and interior angle of a regular polygon is 2: 3, the number of sides of the polygon is


  1. 7

  2. 6

  3. 5

  4. 4


Solution

The correct option is C

5


It is given that the polygon is regular.

      Let exterior angle = 2x°

      Interior angle = 3x° (given)

In a regular polygon,

     interior angle +  exterior angle = 180°

                 3x + 2x  = 180°

                                 5x = 180°

                                   x = 36°

Exterior angle = 2×36°=72°

    

Number of sides (n) = 360°exterior angle

        = 360°72°

        = 5

Hence (C)

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