Question

Ratio of the number of sides of two regular polygons is $5:6$ and the ratio of their each interior angle is $24:25$ Then the number of sides of these polygons are--

• A. $20,24$
• B. $15,18$
• C. $10,12$
• D. $5,6$

Answer 1

The correct option is C $10,12$

Let the number of sides of two regular
polygons are 5n and 6n respectively and
their each interior angle are $24x^{\circ }$ and $25x^{\circ }$
respectively
Then as per question--
$\because$ $\frac{(2\times 5n-4)\times {90}^{\circ }}{(2\times 6n-4)\times {90}^{\circ }}=\frac{5n\times 24x^{\circ }}{6n\times 25x^{\circ }}$
$\Rightarrow$ $\frac{10n-4}{12n-4}=\frac{4}{5}$
$\Rightarrow$ $50n-20=48n-16$
$\Rightarrow$ $(50-48)n=20-16$
$\therefore$ $n=2$
Hence the actual number of sides of these
polygons are = 10 and 12