The outer angle at the vertex A of the triangle ABC is equal to 120 degrees. The inner angle at apex C is 80 degrees.

The outer angle at the vertex A of the triangle ABC is equal to 120 degrees. The inner angle at apex C is 80 degrees. Calculate the outside angle of the triangle at vertex B.

The angle BAD and the angle BAC are adjacent angles, the sum of which is 180. Then the angle BAC = 180 – BAD = 180 – 150 = 30.

Determine the value of the angle ABC in the triangle ABC.

Angle ABC = 180 – BAC – AСB = 180 – 30 – 80 = 70.

The sought external angle CBE is adjacent to the angle ABC, then the angle CBE = 180 – ABC = 180 – 70 = 110.

Answer: The outside angle at the vertex B is 110.