Question : The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively:
Option 1: 6, 12
Option 2: 5, 10
Option 3: 4, 8
Option 4: 7, 14
Correct Answer: 4, 8
Solution :
Given, The ratio between the number of sides of two regular polygons = 1 : 2
And, the ratio between their interior angles = 2 : 3
Let the number of sides be
For a regular polygon, interior angle =
So,
Or,
Or,
and,
Hence, the correct answer is 4, 8.
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