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Question

The ratio between the number of sides of two regular polygons is 3:4 and the ratio between the sum of their interior angles is 2:3. Find the number of sides in each polygon

A
6 and 8
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B
7 and 8
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C
3 and 4
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D
12 and 16
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Solution

The correct option is D 6 and 8
The ratio between the number of sides of two regular polygons is 3:4 and the ratio between the sum of their interior angles is 2:3.
Let number of sides of 1st polygon is n1 and 2nd polygon is n2.
So,
n1n2=34 and 180o(n12)180o(n22)=23
=>n1=34n2 and =>3n16=2n24
=>n1=3n24 and =>n1=2(n2+1)3
Then,
3n24=2(n2+1)3
=>9n28n2=8
=>n2=8
Now,
=>n1=3n24=n1=3×84=6

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