Question

Two regular polygon are such that the ratio between thier number of sides is 1:3 and the ratio of the measure of their interior angles is 4:7 . Find the number of sides of each polygon.
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Answer 1

Answer:Let number of sides of two polygons are n and 2n 

measures of interior angles of x sided regular polygon is x(x−2)×180°

so nn−2×180°2n2n−2×180°=34⇒2(n−2)2n−2=34⇒6n−6=8n−16⇒2n=10⇒n=5

Therefore, number of sides of polygon are 5 and 10.