What is the sum of the outer angles of a regular n-gon if one outer corner is taken at the vertex?

The angles of a triangle add up to 180 °.

That is, <A + <B + <C = 180 °.

Now we write down through the inner corners of the triangle their corresponding outer corners:

180 ° – <A + 180 ° – <B + 180 ° – <C = 180 ° + 180 ° + 180 ° – (<A + <B + <C) = 540 ° – (<A + <B + <C ).

Substitute the sum of the interior angles of the triangle into the resulting expression:

180 ° – <A + 180 ° – <B + 180 ° – <C = 540 ° – (<A + <B + <C) = 540 ° – 180 ° = 360 °.

Answer. The sum of the outer angles of a triangle is 360 °.