In an isosceles triangle ABC with base AC, the outside angle at apex C is 123 degrees. Find the angle ABC.

1. Find the inner angle ACB at vertex C.

180 – 123 = 57 (°) – according to the property of adjacent angles, their sum is 180 °.

2. Angle BAC = 57 (°) – by the property of an isosceles triangle, the angles at the base are equal.

3. Angle ABC = 123 – 57 = 66 (°) – by the property of the outer corner of the triangle.

Or the angle ABC = 180 – 57 * 2 = 180 – 114 = 66 (°) – the sum of the angles of the triangle is 180 °.

Answer: Angle ABC = 66 °.