Question

Two regular polygons are such that the ratio between their number of sides is 1 : 2 and the ratio of measures of their interior angles is 3 : 4. Find the number of sides of each polygon.

• A. $5,10$
• B. $6,12$
• C. $4,8$
• D. $2,3$

Answer 1

The correct option is A $5,10$

Let the number of sides of Polygon 1 $=$ $x$

Let the number of sides of Polygon 2 $=$ $y$

We are given that $\frac{x}{y}$ $=$ $\frac{1}{2}$ ----(1)

Interior angles of Polygon 1 $=$ $\frac{(x-2)\pi }{x}$

Interior angles of polygon 2 $=$ $\frac{(y-2)\pi }{y}$

Taking their ratios, we get

$\frac{y(x-2)}{x(y-2)}$ $=$ $\frac{3}{4}$-----(2)

Solving simultaneous equations (1) and (2),

we get $x=5,y=10$