In triangle ABC, the outside angle at A is 123 degrees and the outside angle at B is 63 degrees. Find the angle C of triangle ABC.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.
Since the sum of the outer and inner angles of the triangle is 180º, then:
∠А = 180º – φ;
∠А = 180º – 123º = 57º.
∠В = 180º – 63º = 117º.
Since the sum of all the angles of the triangle is 180º, then:
∠С = 180º – 57º – 117º = 6º.
Answer: the degree measure of the angle ∠С is equal to 6º.