Question

The ratio between the number of sides of two regular polygons is 1:2. The ratio of the measures of their interior angles is 3:4. How many sides are there in each polygon?​

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

n

n−2

×180°

2n

2n−2

×180°

=

3

4

⇒

2(n−2)

2n−2= 34

⇒6n−6=8n−16

⇒2n=10

⇒n=5

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