An interior angle of a regular polygon is 5 times its exterior

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An interior angle of a regular polygon is 5 times its exterior angle. Then the number of sides of the polygon is

If the number of sides of regular polygon be n, then

Each interior angle =	(2n - 4) × 90°
	n

And each exterior angle =	360°
	n

According to question ,

∴	(2n - 4)	× 90° =	5 × 360°
	n		n

⇒ (2n – 4) = 5 × 4
⇒ 2n – 4 = 20
⇒ 2n = 20 + 4 = 24

⇒ n =	24	= 12
	2