The sum of the angles of a polygon with the number of angles n:
P (n – 2) (1).
The angle between two adjacent sides of the polygon, corresponding to the outer angle p / 7:
P – P / 7.
The sum of the angles of a regular n-gon, each angle of which is equal to P – P / 7:
n (P – P / 7) (2).
Expressions (1) and (2) define the same sum of angles:
P (n – 2) = n (P – P / 7);
n – 2 = n (1 – 1/7);
n – 2 = n – n / 7;
n / 7 = 2;
n = 14.
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