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Question

In a regular pentagon the ratio of interior angle : exterior angle = ___


  1. 2 : 3

  2. 3 : 2

  3. 1 : 3

  4. 3 : 1


Solution

The correct option is B

3 : 2


A pentagon has 5 sides. Since the pentagon is regular, all its angles and sides are equal.

Let the interior angle be x and exterior angle be y.

sum of exterior angles in a polygon is 360

5y = 360

y=3605=72

sum of exterior angle and its respective interior angle in a polygon is 180

x+y=180

x=180y

=18072

=108

Now, interior angleexterior angle = xy=10872=32

Hence, interior angle : exterior angle = 3 : 2

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