Notes
three congruent triangles ii solution

Solution to the Three Congruent Triangles II Puzzle

Solution by Angles on a Straight Line, Isosceles Triangle, and Angles in a Triangle

With the points labelled as above, the congruency of the triangles is so that $A F B$ rotates to $E B D$ which then reflects to $C B D$. Therefore, the angles at $B$ are all the same and so since angles on a straight line add up to $180^\circ$ each must be $60^\circ$. This means that angle $C \hat{B} E$ is $120^\circ$. Since $B E$ and $B C$ are the same length, triangle $E B C$ is isosceles and so since angles in a triangle add up to $180^\circ$, angle $E \hat{C} B$ is $30^\circ$.