Question

The number sides of two regular polygons are in the ratio 2 : 1 and their interior angles are in the ratio 4 : 3. Find the number of sides in each polygon.

• A. 10 and 5
• B. 8 and 6
• C. 10 and 4
• D. 8 and 5

Answer 1

The correct option is A 10 and 5

The ratio between the number of sides of two regular polygons is 2:1 and the ratio of their interior angles is 4:3.
Let number of sides of 1st polygon is $n_1$ and 2nd polygon is $n_2$.
So,
$\frac{n_1}{n_2}=\frac{2}{1}$ and $\frac{\frac{{180}^o(n_1-2)}{n_1}}{\frac{{180}^o(n_2-2)}{n_2}}=\frac{4}{3}$
$=>n_1=2\times n_2$ and $=>3n_1{n}_2-6n_2=4n_2{n}_1-8n_1$
$=>n_1=2n_2$ and $=>n_1{n}_2=8n_1-6n_2$
Then,
$2n_2{n}_2=8\times 2n_2-6n_2$
$=>2{n_2}^2=10n_2$
$=>n_2=5or1$ But $n_2=1$ is not exist therefore $n_2=5$
Now,
$=>n_1=2n_2=2\times 5=10$