n-gon

Gabo draws n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?

Correct answer:

n =  6

Step-by-step explanation:

$$\begin{gathered} S_n=180(n-2)={\displaystyle \frac{70+170}{2}}n \\ n={\displaystyle \frac{360}{180-{\displaystyle \frac{70+170}{2}}}}=6 \end{gathered}$$

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