In an isosceles triangle ABC with a base BC, angle A is 54 degrees. Find the value of the outer angle at the vertex C.

In an isosceles triangle, the angles at the base are equal. In triangle ABC, the base is side BC. Hence, the angles at the base are ∠B and ∠C. The angle at the vertex of the triangle ABC is ∠A.

The angles of a triangle add up to 180 °.

∠A + ∠B + ∠C = 180 °;

∠B + ∠C = 180 ° – ∠A;

∠B + ∠C = 180 ° – 54 °;

∠B + ∠C = 126 °;

since angles B and C are equal, then ∠C = ∠B = 126 ° ： 2 = 63 °.

The outer corner and the inner corner at one vertex of the triangle form adjacent angles. The sum of adjacent angles is 180 °. This means that the outer angle at the vertex C is 180 ° – 63 ° = 117 °.

Answer. 117 °.