The sum of the outer angles of triangle ABC at vertices A and B, taken one for each vertex

The sum of the outer angles of triangle ABC at vertices A and B, taken one for each vertex, is 240 degrees. Find the corner C.

The outer corner of a triangle is an angle adjacent to one of its vertices. The sum of the outer and inner angles of a triangle with a common apex is equal to 180º, and is a flat angle. That’s why:

φ = 180º – ∠А;

∠А = 180º – φ.

Since the sum of the external angles at the vertices A and B is equal to 240º, and the sum of the unfolded angles at these vertices is 360º, then:

∠А + ∠В = 360º – 240º = 120º.

The sum of all the angles of the triangle is 180º, so:

∠С = 180º – (∠А + ∠В);

∠С = 180º – 120º = 60º.

Answer: the angle ∠С is equal to 60º.