In an isosceles triangle ABC with a base BC, the outer angle at apex A is 132 °. Find the outside angle at vertex B.

The angle BAC is adjacent to the angle СAK, the sum of which is 180, then the angle BAC = 180 – СAK = 180 – 132 = 48.

Since the triangle ABC is isosceles, its angles at the base of the AC are equal. Angle ABC = AСB.

The sum of the inner angles of the triangle is 180, then the angle ABC = ACB = (180 – BAC) / 2 = (180 – 48) / 2 = 66.

The sought angle ABE adjacent to the angles ABC, then the angle ABE = 180 – ABC = 180 – 66 = 114.

Answer: The outer angle at the vertex B is equal to 114.