Question

73 Each angle of a regular polygonis 4/5 of each angle of another polygon. And, the number of its sides is half that of the other. How many sides does it have?​

Answer 1

Step-by-step explanation:

Given ratio of numbers of sides of two regular polygin is 1:2.

Let numbers of sdes be a,2a.

Interior angle of regular polygon with a sides=180°-360°/a

Interior angle of regular polygon with 2a sides=180°-360°/2a

Acording to question..

((180°-360°/a))/((180°-180°/a))=2/3

(a-2)/(a-1)=2/3

3a-6=2a-2

a=4

Hence required regular polygons are square and octagon.

I hope this is helpful