The sum of the angles of an isosceles triangle CDE is 180∘. The bisector EK is drawn. The DEK angle is 52∘. Find corner C.

Triangle CDE – isosceles;
EK – bisector;
DEK angle = 52 °;
Angle С -? °;
So, a bisector is a line that goes out from the vertex of an angle and divides the given angle into two equal parts. Thus, we find what the angle E is equal to:
52 + 52 = 104 °;
The triangle is isosceles, which means that some two angles in it are equal.
Note that a triangle cannot have two angles equal to 104 °, since the sum of all the angles of a triangle is always 180 °. So the angle E is the largest angle.
Find two equal angles in a triangle:
180 – 104 = 76 ° – the sum of the angles;
86; 2 = 38 ° – angle С;
Answer: 38 °.