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

Question

Accepted Answer

10 — Easy Use the interior-angle formula $\dfrac{(n-2)180^\circ}{n}$. With sides $n$ and $2n$ and angle ratio $3:4$, form one equation and solve for $n$, then double it. 1 Set up the ratio (A has $n$ sides, B has $2n$): $$\dfrac{\frac{(n-2)180}{n}}{\frac{(2n-2)180}{2n}}=\dfrac{3}{4}$$ 2 Simplify &mdash; the $180$ cancels and the $2n$ tidies the second fraction: $$\dfrac{(n-2)/n}{(2n-2)/2n}=\dfrac{2(n-2)}{2n-2}=\dfrac{n-2}{n-1}=\dfrac{3}{4}$$ 3 Cross-multiply and solve: $$4(n-2)=3(n-1)\ \Rightarrow\ 4

CAT 2022 Slot 2 — QA Question 19

Answer & solution