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
• B. 3 and 4
• C. 9 and 12
• D. 8 and 6

Answer 1

Answer: (A), (D)

Sum of interior angles regular polygons = $(n-2)\ast 180$

sides of two regular polygons= $x$ and $y$

So, $x/y=3/4$

$x=3y/4$

Sum of interior angles regular polygons $\left(x\right)=(x-2)\ast 180$

Sum of interior angles regular polygons $\left(y\right)=(y-2)\ast 180$

$(x-2)\ast 180/(y-2)\ast 180=2/3$

$x-2/y-2=2/3$

$3y/4-2/y-2=2/3$

$3y-8/y-2=8/3$

$9y-24=8y-16$

$y=8$

$x=3y/4=3\ast 8/4=6$

Answer (A) 6 and 8, (D) 8 and 6.