The ratio between the number of sides of two regular polygon is 1:2

18.

If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y is 

B.

4 : 3

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10 Questions 10 Marks 10 Mins

Given:

The ratio of the number of sides of two polygons is 2 : 3

And, the ratio between their interior angles is 1 ∶ 2.

Formula used:

Sum of interior angles of a polygon of sides n = (n - 2) × 180°

Calculation:

Let the number of sides of given polygons be 2n and 3n respectively.

Now, ATQ

(2n - 2) × 180°:(3n - 2) × 180° = 1 : 2

⇒ (2n - 2) : (3n - 2) = 1:2

⇒ 4n - 4 = 3n - 2

⇒ 4n - 3n = 4 - 2

⇒ n = 2

⇒ 2n = 4 and 3n = 6

∴ The total number of sides in given polygons is 4 and 6.

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$\Rightarrow 4n-3n=8-3$

$\therefore n=5$

Therefore, the number of sides in each polygon is $n$ and $2n$, which is $5$ and $10$ respectively.