A and B are two regular polygons with $a$ and $b$ sides respectively. The interior angle of polygon A is 3 times the exterior angle of polygon B. Which of the following is correct?
Answer and solution
Correct answer: C
Solution
Interior angle of A $= \dfrac{180(a-2)}{a}$, exterior angle of B $= \dfrac{360}{b}$.
Condition: $\dfrac{180(a-2)}{a} = 3 \times \dfrac{360}{b}$.
Try $a = 6$ (hexagon): interior $= 120^\circ$. Then $120 = \dfrac{1080}{b} \Rightarrow b = 9$ (valid polygon). Interior angle of A $= 120^\circ$.
Condition: $\dfrac{180(a-2)}{a} = 3 \times \dfrac{360}{b}$.
Try $a = 6$ (hexagon): interior $= 120^\circ$. Then $120 = \dfrac{1080}{b} \Rightarrow b = 9$ (valid polygon). Interior angle of A $= 120^\circ$.