Correct answer and explanation required
The number of sides of a regular polygon is double that of the another and the magnitude of its angle is also double that of the other. Then the number of sides of polygon gre
a) 12
b) 10
c) 8
d) 3
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Let's denote the number of sides of the first polygon as n and the number of sides of the second polygon as m. According to the given information, we have two conditions:
1. The number of sides of the first polygon is double that of the second polygon: n = 2m.
2. The magnitude of the angle in the first polygon is double that of the second polygon.
In a regular polygon, each interior angle can be calculated using the formula:
__Interior angle = (n - 2) _ 180 / n_*
Using this formula, we can set up the following equation based on the information given:
__(n - 2) _ 180 / n = 2 _ ((m - 2) _ 180 / m)_*
Simplifying this equation, we get:
__(n - 2) / n = 2 _ (m - 2) / m_*
Cross-multiplying, we have:
__m _ (n - 2) = n _ (2 _ (m - 2))_*
Expanding and simplifying further:
__m _ n - 2m = 2n - 4_*
Rearranging the terms:
__m _ n - 2n = 2m - 4_*
Factoring out n and m:
*n _ (m - 2) = 2 _ (m - 2)*
Simplifying, we have:
*n = 2*
Since n represents the number of sides of the first polygon, we have found that it is equal to 2. Therefore, the number of sides of the second polygon, m, would be half of n, which is 1.
However, a polygon cannot have 1 side, so this case is not possible. Hence, there is no valid solution to the given conditions.
Therefore, the answer is *none of the above (no valid solution)*.