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
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.