Question

Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measure of their interior angles is 3:4. The number of sides of each polygon is

• A. 5, 10
• B. 6, 12
• C. 4, 8
• D. 2, 3

Answer 1

The correct option is A 5, 10

Let the number of sides of the regular polygon be 'n' and 2n.
$\therefore$ Their interior angles are
$(\frac{2n-4}{n}\times {90}^0)$ and $(\frac{2\left(2n\right)-4}{2n}\times {90}^0)$
The ratio of measures of interior angles is 3 : 4
$\frac{\left(\frac{2n-4}{n}\right)\times {90}^0}{\left(\frac{2\left(2n\right)-4}{2n}\right)\times {90}^0}=\frac{3}{4}$
$\Rightarrow \frac{\left(\frac{2n-4}{n}\right)}{\left(\frac{4n-4}{2n}\right)}=\frac{3}{4}$
$\Rightarrow \frac{2n-4}{n}\times \frac{2n}{4n-4}=\frac{3}{4}$
$\Rightarrow \frac{n-2}{n-1}=\frac{3}{4}$
$\Rightarrow 4n-8=3n-3$
$\Rightarrow n=5$