The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.
Ratio of sides of two regular polygons = 3 : 4
Let sides of first polygon = 3n
and sides of second polygon = 4n
∴ Sum of interior angles of first polygon =(2×3n−4)×90o=(6n−4)×90o
and sum of interior angle of second polygon
=(2×4n−4)×90o=(8n−4)×90o∴(6n−4)×90o(8n−4)×90o=23⇒6n−48n−4=23⇒18n−12=16n−8⇒18n−16n=−8+12⇒2n=4⇒n=2
∴ No. of sides of first polygon =3n=3×2=6
and no. of sides of second polygon
=4n=4×2=8