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How many sides does a regular polygon have whose interior and exterior angle are in the ratio 2 : 1 ?

A. 3

B. 5

C. 6

D. 12

Answer: Option C

Solution(By Examveda Team)

Each exterior angle of n sided polygon is
$${\text{ = }}\left( {\frac{{360}}{n}} \right)$$
And each interior angle of n sided polygon
$$\eqalign{ & {\text{ = }}\frac{{\left( {n - 2} \right) \times 180}}{n} \cr & \therefore \frac{{\frac{{\left( {n - 2} \right) \times 180}}{n}}}{{\frac{{360}}{n}}} = \frac{2}{1} \cr & \Rightarrow \frac{{\left( {n - 2} \right)}}{2} = 2 \cr & \Rightarrow n - 2 = 4 \cr & \Rightarrow n = 6 \cr} $$

This Question Belongs to Arithmetic Ability >> Ratio

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Comments ( 1 )

  1. Muhammad Safyan
    Muhammad Safyan :
    3 years ago

    Taking the interior and exterior angles as 2x° and x°, we get 2x° + x° = 180° => x = 60°

    Number of sides of a regular polygon is given by 360/each exterior angle = 360/60 = 6.

    So the given regular polygon has 6 sides.

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