Nine matchsticks are arranged into three identical equilateral triangles as is shown. It is possible to move just two matchsticks in order to get only two equilateral triangles. No loose matchsticks are allowed.
If the initial mutual angle between the two moved matchsticks is X and the mutual angle between them at the solution is Y, what is the sum X + Y?
As is shown in the illustration, the mutual angle between the moved matchsticks at the beginning is 60 degrees. At the solution their mutual angle is also 60 degrees. Thus, their sum is 120 degrees.