# Angles in a Cube II

Let denote the vertices of a cube ABCD (for the bottom face) and A'B'C'D' (for the top face), with A' above A, etc. Let K, L, M denote the midpoints of A'B', B'C' and CC'. What is the angle KLM?

What if applet does not run? |

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Copyright © 1996-2018 Alexander Bogomolny### Solution

Check the "6 segments" box. You'll see a hexagon with all sides equal and clearly all angles also equal as they may be overlayed by rotating the cube.

What if applet does not run? |

The applet helps verify that the hexagon is planar: all its vertices lie in the same plane, implying that the hexagon is regular, so that the angle in question is 120°.

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Copyright © 1996-2018 Alexander Bogomolny66541265