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

Let the sides are $3 n$ and $5 n$.
$ \frac{180 n-120}{180 n-720}=\frac{5}{6} $
$1080 n-720=900 n-360$
$ 1080 n-900 n=-360+720 $
$180 n=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 $6+10=16$.