${C}$ and ${D}$ are two points on the same side of a straight line ${AB}$. Find a point X on AB such that the angles ${CXA}$ and ${DXB}$ are equal.
Note: This is how I have approached the problem. We take two points randomly on the same side of a straight line as shown in figure below.
Now, a line is drawn parallel to ${AB}$ passing through ${C}$ which intersects ${CX}$ at ${E}$. When ${EX=DX}$, then ${\angle{EXA}=\angle{DXB}}$ implying that ${\angle{CXA}=\angle{DXB}}$. From this, we get the fact that ${X}$ should be positioned such that ${EX=DX}$. But from here onward I'm stuck! My thinking also may be wrong! Please help me! Even if someone points me in the right direction, it will be highly helpful. Thank you!
Reflect $C$ across $AB$, to $C'$. $C'D$ now crosses $AB$ at X.