Question

The ratio of the number of sides of two regular polygon is 5:8, and the ratio of their interior angle is 1:2.Find the number of sides in each polygon.​

Answer 1

Answer:

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Step-by-step explanation:

Each interior angle =

n

(2n−4)×90

∘

According to the question,

2n

(2×2n−4)×90

∘

n

(2n−4)×90

∘

=

3

2

(Ratio of number of sides is 1:2)

⇒

4n−4

(2n−4)×2

=

3

2

⇒

4n−4

2n−4

=

3

1

⇒6n−12=4n−4⇒6n−4n=12−4=8

⇒2n=8⇒n=4

Hence, number of sides in polygons are 4 and 8 respectively.