MathNet 2020 — Math Olympiad Vault — Part 01 Question 12

Let $ABCD$ be a parallelogram with $\angle ABC = 105^\circ$. Inside it there is a point $E$ such that triangle $BEC$ is equilateral and $\angle CED = 135^\circ$. Let $K$ be the midpoint of side $AB$. Calculate angle $BKC$.