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.
10 and 5
10 and 4
8 and 5
8 and 6

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-10 and 510 and 48 and 58 and 6

Toppr Admin · Accepted Answer

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 $=> 3 n_{1} n_{2} - 6 n_{2} = 4 n_{2} n_{1} - 8 n_{1}$
$=> n_{1} = 2 n_{2}$ and $=> n_{1} n_{2} = 8 n_{1} - 6 n_{2}$
Then,
$2 n_{2} n_{2} = 8 \times 2 n_{2} - 6 n_{2}$
$=> 2 {n_{2}}^{2} = 10 n_{2}$
$=> n_{2} = 5 o r 1$ But $n_{2} = 1$ is not exist therefore $n_{2} = 5$
Now,
$=> n_{1} = 2 n_{2} = 2 \times 5 = 10$

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.10 and 510 and 48 and 58 and 6

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.
10 and 5
10 and 4
8 and 5
8 and 6