Question

The numbers of sides of two regular sides of two regular polygons are in the ratio 4: 5 and their interior angles are in the ratio 15: 16, find the difference in the number of sides of the polygons.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B

2

Let the number of sided in polygon A and B be x and y respectively.

As per question, ratio of their side is 4: 5

So, x: y = 4: 5

5x=4y$\dots \left(i\right)$

Ratio of their interior angle is 15: 16.

Interior angle of polygon $A=\left\{\frac{2(x-2)}{x}\right\}\times {90}^{\circ }$

Interior angle of polygon $B=\left\{\frac{2(y-2)}{y}\right\}\times {90}^{\circ }°$

$\frac{\left\{\frac{2(x-2)}{x}\right\}\times {90}^{\circ }}{\left\{\frac{2(y-2)}{y}\right\}\times {90}^{\circ }}=15:16$

$\Rightarrow 16yx-32y=15xy-30x\Rightarrow yx=32y-30x\Rightarrow yx=32y-24y(fromeq.(i\left)\right)\Rightarrow yx=8y\Rightarrow x=8So,y=10Hence,differenceintheside=(10-8)=2$