Notes
two squares inside an equilateral triangle solution

Two Squares Inside an Equilateral Triangle

Solution by Interior Angles of Regular Polygons

The line segment $A B$ is parallel to the base of the equilateral triangle, so triangle $A B C$ is also equilateral. Therefore, line segments $A C$ and $A B$ are of equal length, so triangle $A C D$ is isosceles. The angle $D \hat{A} C$ is $90^\circ + 60^\circ = 150^\circ$ as it is formed from interior angles in regular polygons, so angle $C \hat{D} A$ is $15^\circ$. This leaves $75^\circ$ for angle $F \hat{D} C$ and so angle $E \hat{D} C$ is $45^\circ + 75^\circ = 120^\circ$.