Question

Two regular polygons are such that the ratio of the measures their interior angles is $5:6$ and the ratio between their number of sides is $3:5$. Then the sum of the number of sides of each polygon is__

Answer 1

Answer: 16

Let the sides are $3n$ and $5n$.
$\frac{180n-120}{180n-720}=\frac{5}{6}$
$1080n-720=900n-360$
$1080n-900n=-360+720$
$180n=360$
$n=\frac{360}{180}$
$\therefore n=2$
So, the sides are $3\times 2=6$ and $5\times 2=10$
$\therefore$ Sides are 6 and 10 . The sum is $6+10=16$.