In triangle ABC, angle C = 30 degrees, and outside angle at vertex A. Find the unknown angles of the triangle.

Given: tr-to ABC, angle C = 30 degrees, external angle at apex A is equal to 120 degrees.
Find: angle A and angle B.
Solution: The sum of the outer and inner angles is 180 degrees. Since the external angle at the vertex A = 120, then the angle A = 180 – 120 = 60. The sum of the angles of the triangle is 180. Since the angle C = 30 degrees, and the angle A = 60 degrees, then the angle B = 180 – (angle A + angle C) = 180 – (60 + 30) = 180 – 90 = 90 degrees.
Answer: angle A = 60 degrees, angle B = 90 degrees