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Question

The ratio between the number of sides of two regular polygons is 1:2. The ratio of the measures of their interior angles is 3:4. How many sides are there in each polygon?


A
7 and 10
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B
5 and 15
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C
5 and 10
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D
10 and 12
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Solution

The correct option is C 5 and 10
Given: The sides of the two regular polygons are in the ratio 1:2.

Let the number of sides of the polygons be n and 2n respectively

The interior angles of these polygons are in the ratio 3:4.

The measure of each interior angle for a regular polygon with n sides is given by (n2)×180n

Therefore, the measure of each interior angle of the given polygons will be (n2)×180n and (2n2)×1802n respectively.

Also, the ratio of the interior angles is 3:4.

(n2)×180n÷(2n2)×1802n=34

n2n1=34

4n8=3n3

4n3n=83

n=5

Therefore, the number of sides in each polygon is n and 2n, which is 5 and 10 respectively.


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