The correct option is D 5 and 10
Given: The sides of the two regular polygons are in the ratio 1:2.
Let the number of sides of the polygons be n and 2n respectively
The interior angles of these polygons are in the ratio 3:4.
The measure of each interior angle for a regular polygon with n sides is given by (n−2)×180∘n
Therefore, the measure of each interior angle of the given polygons will be (n−2)×180∘n and (2n−2)×180∘2n respectively.
Also, the ratio of the interior angles is 3:4.
∴(n−2)×180∘n÷(2n−2)×180∘2n=34
⇒n−2n−1=34
4n−8=3n−3
On solving the above equation, we get n=5
Therefore, the number of sides in each polygon is n and 2n which is 5 and 10 respectively.