In the triangle ABC, the sides AC and BC are equal. The outer angle at the vertex B is equal to 116 °. Find the angle C.

Let’s find the angle ABC of our triangle f. This angle is adjacent to the outer angle at the vertex B and its degree measure is equal to:
Angle ABC = 180 ° – 116 ° = 64 °.
By condition, the two sides of the triangle are equal, it follows from this uj that it is isosceles and the angles at the base are equal:
Angle ABC = angle CAB = 64 °.
The sum of the angles of a triangle is 180, two angles are known, we find the third angle at the apex of an isosceles triangle:
BCA angle = 180 ° – 2 * 64 = 180 ° – 128 ° = 52 °.
Answer: Angle C is 52 °.