Angle between two line segments of a cube.

[IHateFactorial]

Given a cube, choose a vertice and draw 2 of the three possible diagonals. What is the measure of the angel between those two diagonals?

Proposed answer: We can say that both diagonals touch vertice A, to give it a name. We can also call the endpoints of both diagonals B and C. If we imagine the diagonal that goes through points B and C, we can see that the points A, B, and C, all lie on the same plane and that they form an equilateral triangle. The measure of every angle in an equilateral triangle is 60°. The answer, I believe, is 60°.

Is this right? (Whether it is or isn't right, how can I apply this to any two line segments that share a point on the cube)

 

[Greg]

It's correct, assuming "diagonal" means the diagonal of a face of the cube and the diagonals emanate from the chosen vertex. In order for me to answer the remaining question you'll have to be more specific about what application you are looking for. Do you mean finding the angles and lengths of triangles constructed in a similar fashion? By the way, any three points are contained in the same plane.