Sizing Up - Futility Closet

Sizing Up

Two lines divide this equilateral triangle into four sections. The shaded sections have the same area. What is the measure of the obtuse angle between the lines?

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Triangles CAM and ABN have the same area. Rotating triangle ABC 120° takes CAM into ABM1. Since ABN and ABM1 have the same area and both N and M1 fall on BC, N = M1. Since rotating CM produces AN, the angle between them is 120°, or 180° – 120° = 60°, which is the same. (Posed by V. Proizvolov in Math Horizons, Spring 1994.)

November 25, 2014November 30, 2014 | Puzzles