# Two Squares Inside an Equilateral Triangle +-- {.image} [[TwoSquaresInsideanEquilateralTriangle.png:pic]] > Two squares inside an equilateral triangle. What’s the angle? =-- ## Solution by [[Interior Angles of Regular Polygons]] +-- {.image} [[TwoSquaresInsideanEquilateralTriangleLabelled.png:pic]] =-- 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 $45^\circ + 75^\circ = 120^\circ$.