Discussion

Explanation:

Interior angle of a n-sided regular polygon = $\frac{(n-2)\times 180°}{n}$

Let the number of sides of polygon A and B be n and 2n respectively.

⇒ $\frac{{\displaystyle \frac{(n-2)\times 180°}{n}}}{{\displaystyle \frac{(2n-2)\times 180°}{2n}}}$ = $\frac{3}{4}$

⇒ $\frac{n-2}{n-1}$ = $\frac{3}{4}$

⇒ 4n – 8 = 3n – 3

⇒ n = 5

∴ Number of sides of polygon B = 2n= 10.

Hence, 10.

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