The sum of the two outer angles of a triangle is 240 degrees. Find the inside corner of the triangle

The sum of the two outer angles of a triangle is 240 degrees. Find the inside corner of the triangle that is not adjacent to these outside corners.

Let’s designate the inner angles of the triangle A, B, C, and the outer corresponding angles A1, B1, C1.
We know that the sum of the two outer angles is 240 degrees, i.e. A1 + B1 = 240.
Angles A and A1, B and B1 are adjacent. The sum of adjacent angles is 180 degrees.

A + A1 = 180, B + B1 = 180;

A + A1 + B + B1 = 360;

A + B = 360 – (A1 + B1);

A + B = 360 – 240 = 120.

The angles of a triangle add up to 180 degrees.

A + B + C = 180;

C = 180 – (A + B);

C = 180 – 120 = 60.

Answer. 60.