# The outer angle of a regular n-gon is π / 7 Find the number of sides of the polygon

October 6, 2021 | education

| 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.

Answer: 14

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