Problem 555: Parallel lines, Angles, Sum
Level: High School, College, Math Education The figure shows line L_{1} parallel to line L_{2} with angles a, x, y, and
z. Find x + y + z.
Geometry problem solving
Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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