Problem 556: Quadrilateral, Diagonal, Angles, Auxiliary Lines
Level: High School, College, Math Education The figure shows a quadrilateral ABCD with diagonal AC and BC = CD. If
angle CAD = 39 degrees, angle ACB = 21 degrees, and angle ADC = 78
degrees, find angle BAC.
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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