Question

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Correct option is

Let number of sides of 1st polygon is $n_{1}$ and 2nd polygon is $n_{2}$.

So,

$n_{2}n_{1} =12 $ and $n_{2}180_{o}(n_{2}−2) n_{1}180_{o}(n_{1}−2) =34 $

$=>n_{1}=2×n_{2}$ 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,

$2n_{2}n_{2}=8×2n_{2}−6n_{2}$

$=>2n_{2}_{2}=10n_{2}$

$=>n_{2}=5or1$ But $n_{2}=1$ is not exist therefore $n_{2}=5$

Now,

$=>n_{1}=2n_{2}=2×5=10$

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