In triangle ABC, sides AB and BC are equal, and the outer head at apex C = 123 degrees. Find the value of angle B.

Since in this triangle the sides AB and BC are equal, then this triangle is isosceles, and in an isosceles triangle the angles at the base are equal:

∠А = ∠С.

Since the sum of the outer and inner angles of the triangle at one vertex is 180º, and the outer angle at the vertex C is 123º, then:

∠С = 180º – φ;

∠С = 180º – 123º = 57º;

∠А = ∠С = 57º.

Since the sum of all angles of a triangle is 180º, then:

∠В = 180º – ∠А – ∠С;

∠В = 180º – 57º – 57º = 66º.

Answer: the angle ∠B is equal to 66º.