This problem was asked from 8th and 9th graders in a contest.
You have an quadrilateral $ABCD$ with $AB=4x-y$, $BC=3x-4$, $CD=y$, and $DA=5x-2$. You draw a line $BD$ which makes a right triangle with $\angle CBD=36°$ and in the triangle $ABD$ $\angle DBA=126°$. Solve for $x$.
I was able to solve this with a calculator but this problem is supposed to be solved without one. I tried to find an answer to this problem online but I couldn't find one, probably because my math vocab in English isn't that great.