The number 10

The number of sides of two regular polygons differ by 1 the sum of the interior angles of the polygons is in the ratio of 3:2 calculate the number of sides of each polygon.

Correct answer:

n₁ =  4
n₂ =  5

Step-by-step explanation:

$$\begin{gathered} n_2-n_1=1 \\ {s}_2:s_1=3:2 \\ {s}_n=180(n-2) \\ {s}_2:s_1=3:2 \\ 2\cdot 180(n_2-2)=3\cdot 180(n_1-2) \\ 2\cdot 180((n_1+1)-2)=3\cdot 180\cdot (n_1-2) \\ 2\cdot 180\cdot ((n_1+1)-2)=3\cdot 180\cdot (n_1-2) \\ 180n_1=720 \\ {n}_1=\frac{720}{180}=4 \\ {n}_1=4 \end{gathered}$$

$$\begin{gathered} n_2=n_1+1=4+1=5 \\ \text{ Verifying Solution: } \\ d=n_2-n_1=5-4=1 \\ {s}_1=180\cdot (n_1-2)=180\cdot (4-2)=360{}^{\circ } \\ {s}_2=180\cdot (n_2-2)=180\cdot (5-2)=540{}^{\circ } \\ r=s_2:s_1=540:360=\frac{3}{2}=1\frac{1}{2}=1.5=3:2 \end{gathered}$$

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