Question

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

Answer 1

The correct answer is :10
Regular polygons A and B have interior angles in the ratio $3\ratio4$.Let's denote the number of sides of polygon A as 'n' and the number of sides of
polygon B as '2n' (since the ratio of the number of sides is $1\ratio2$).
The sum of the interior angles of a polygon is given by the formula $(n - 2)\times180\degree$.For a regular polygon,each interior angle is given by $\frac{[(n - 2)\times180]}{n} degrees$.
According to the given ratio of interior angles, we have:
$\frac{[(n - 2)\times180]}{n}\ratio\frac{[(2n - 2)\times180]}{(2n)}=3\ratio4$
Cross-multiplying and simplifying:
4(n-2)=3(2n-2)
Expanding and solving for 'n':
4n-8=6n-6
2n=2
n=5
So, polygon A has 5 sides, and polygon B has $2\times5=10$ sides.