How many sides does a regular polygon have whose interior

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

Let interior angle = I and exterior angle = E
According to questions,

I	=	2	⇒ 2E = I.1 or, E =	I
E	=	1	⇒ 2E = I.1 or, E =	2

But I + E = 180°

I +	I	= 180
	2

3	I = 180
2

I =	2	× 180
	3

I = 120°
We know that each interior angle of a regular polygon of n sides is given by

I =	n − 2	× 180°
	n

120° =	n − 2	× 180°
	n

⇒	n − 2	=	120°	=	2
	n		180°		3

⇒ 3n – 6 = 2n ⇒ n = 6