n-gon

Gabo draw 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 result:

n =  6

Solution:

Sn=180(n2)=70+1702n  n=36018070+1702=6S_n = 180(n-2) = \dfrac{ 70 + 170} {2} n \ \\ \ \\ n = \dfrac{ 360}{180 - \dfrac{ 70 + 170} {2}} = 6



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