In triangle ABC, the angle A is 40 degrees, the outer angle about the vertex B is 102 degrees. Find the corner C.

Answer: 62 degrees.
Explanation of the solution to the problem: first you need to find the inner angle B. There is a theorem that the inner angle is 180 degrees minus the outer angle, thus the inner angle B:
B = 180 – 102 = 78 degrees.
Next, you need to use the theorem on the sum of the angles of a triangle, which states that the sum of the inner angles of a triangle is 180 degrees, that is:
A + B + C = 180
Hence:
C = 180 – B – A = 180 – 78 – 40 = 62 degrees.