In an isosceles triangle KLM with base KM, the angle at the apex M is 32 degrees. Find the outside angle at the vertex L.

Apex angle M is the angle at the base. Find the angle L – the top of an isosceles triangle:
∠ L = 180 ° – 2 * 32 = 116 °.
The outer corner is adjacent, its value is:
∠ L ext. = 180 ° – ∠ L = 180 ° – 116 ° = 64 °.
You can solve the problem knowing the property of the outer corner of the triangle. Its degree measure will be equal to the sum of the two angles of the triangle that are not adjacent to it. In our case, these are:
∠ L ext. = ∠ M + ∠ K = 2 * 32 ° = 64 °.
Answer: the external angle at the vertex L is 64 °.