The ratio 21

The ratio between the number of sides of two regular polygon is 1:2 and ratio of sum of their interior angles is 2:3. Find their number of sides.

Correct answer:

a =  0.5
b =  1

Step-by-step explanation:

$$\begin{gathered} a:2a \\ a:2a=1:2 \\ s=(n-2)\cdot 180{}^{\circ } \\ {s}_1=(a-2)\cdot 180 \\ {s}_2=(2a-2)\cdot 180 \\ {s}_1:s_2=2:3 \\ 3s_1=2s_2 \\ 2\cdot (a-2)\cdot 180=3\cdot (2a-2)\cdot 180 \\ 2\cdot (a-2)=3\cdot (2a-2) \\ 2\cdot (a-2)=3\cdot (2\cdot a-2) \\ 4a=2 \\ a=\frac{2}{4}=0.5 \\ a=\frac{1}{2}=0.5 \end{gathered}$$

$b=2\cdot a=2\cdot 0.5=1$

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