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.
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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.