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Question : Two regular polygons are such that the ratio between their number of sides is 1 : 2 and the ratio of measures of their interior angles is 3 : 4. Then the number of sides of each polygon is:

Option 1: 10 and 20

Option 2: 4 and 8

Option 3: 3 and 6

Option 4: 5 and 10


Team Careers360 10th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

Correct Answer: 5 and 10


Solution : Given that the sides of the two regular polygons are in the ratio 1 : 2.
The interior angles of these polygons are in the ratio 3 : 4
Let the number of sides of the polygons be $n$ and $2n$ respectively.
The sum of interior angles for a $n$-sided regular polygon = $\frac{(n-2)\times 180^\circ}{n}$
So, $\frac{(n-2)\times 180^\circ}{n}\div\frac{(2n-2)\times 180^\circ}{2n} = \frac{3}{4}$
Or, $\frac{n-2}{n-1}=\frac{3}{4}$
Or, $n=5$
and, $2n=10$
Hence, the correct answer is 5 and 10.

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