In triangle ABC, the outer angle at the vertex B is 78 degrees, the angle A = 42 degrees. Find the value of the angle C.

First way.

The outer angle of a triangle is equal to the sum of its inner angles that are not adjacent to it.

Angle СВD = AСВ + СAВ.

Angle AСВ = СВD – СAВ = 78 – 42 = 36.

Second way.

The angle ABC adjacent to the angle СВD, the sum of which is 180, then the angle ABC = 180 – 78 = 102.

The sum of the inner angles of the triangle is 180, then the angle ACB = (180 – ABC – CAB) = (180 – 102 – 42) = 36.

Answer: The angle C is 36.