# Label something with a variable

In the problem below, it seems we are stuck right away.

However, notice that the base angles of triangle $$BCA$$ are congruent. Also, notice that the base angles of triangle $$BCD$$ are congruent. Focusing on angle $$DCB,$$ you may notice the base angles of triangle $$BCD$$ are equal to the angles of triangle $$BCA,$$ plus some value. Let's call that unknown value $$y.$$ After making this creative step, the rest of the solution falls out. Many puzzles can be solved in this way.