The number of sides in two regular polygons are in the ratio

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The number of sides in two regular polygons are in the ratio 5 : 4 and the difference between each interior angle of the polygons is 6°. Then the number of sides are

1. 15, 12
2. 5, 4
3. 10, 8
4. 20, 16

Correct Option: A

The ratio of number of sides in two regular polygons = 5 : 4
Let the number of sides be 5k and 4k respectively.
Difference between each interior angle of the polygons = 6°

⇒	(2 × 5k - 4)90°	-	(2 × 4k - 4) × 90°	= 6°
	5n		4n

	∴ Each interior angle =		2n - 4		× 90°
			n

⇒ (10k – 4) × 360° – (8k – 4) × 450° = 20k × 6°
⇒ (10k – 4) × 12 – (8k – 4)15 = 4k
⇒ 120k – 48 – 120k + 60 = 4k
⇒ 4k = 12 ⇒ k = 3
∴ Number of sides = 15 and 12