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Question

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


A

2 : 3

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B

1 : 3

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C

3 : 2

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D

3 : 1

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Solution

The correct option is C

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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