An equilateral triangle and three squares. What’s the angle?

Solution

The angle is 60°.

This elegant solution was provided by Ignacio Larrosa Cañestro. It uses symmetry and parallel lines alone.

First, the horizontal leg of the angle is parallel to the base of the triangle, because of reflection symmetry in the vertical axis through its top vertex.

The other leg of the angle is parallel to the left side of the triangle, also because of reflection symmetry in the line perpendicular to it through the opposing vertex.

Now evidently the triangle sides make an angle of 60°, so our original angle must also be 60°.