Regular polygons A and B have number of sides in the ratio 1:2 and interior angles in the ratio 3:4. Then the number of sides of B equals

Question

UPSC Quizroom · Accepted Answer

Let the number of sides of polygon A = n.
Then polygon B has 2n sides (ratio 1:2 given).

Interior angle of a regular polygon with k sides = ((k − 2) × 180) / k

Interior angle of A = ((n − 2) × 180) / n
Interior angle of B = ((2n − 2) × 180) / (2n) = ((n − 1) × 180) / n

Given: ratio of interior angles = 3 : 4

So,
(n − 2) / (n − 1) = 3 / 4

Cross-multiply:
4(n − 2) = 3(n − 1)

4n − 8 = 3n − 3
n = 5

Number of sides of polygon B = 2n = 10

Final Answer: 10

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