In a regular polygon, the exterior and interior angles are

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In a regular polygon, the exterior and interior angles are in the ratio 1 : 4. The number of sides of the polygon is

1. 10
2. 12
3. 15
4. 16

Correct Option: A

Given , The ratio of exterior and interior angles = 1 : 4
Let the exterior angle be y, then interior angle will be 4y.
We know that , Interior angle + Exterior angle = 180°
∴ y + 4y = 180°

⇒ y =	180	= 36°
	5

∴ Interior angle = 4y = 4 × 36° = 144°

Interior angle of a polygon =	2n - 4	× 90°
	n

144° =	2n - 4	× 90°
	n

⇒ 144°n = 180°n – 360°
⇒ 180°n – 144n = 360°
⇒ 36°n = 360°

∴ n =	360°	= 10
	36°