###### Online Geometry Problem 986: Triangle, Median, Midpoint, Equal Angles, 45 Degrees. Level: High School, College, Mathematics Education

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 The figure below shows a triangle ABC with the median BD such that angles A and DBC are equal. If angle BDC is 45 degrees, find the measure of angle A. Try to use elementary geometry (Euclid's Elements.)       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 ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given." ont>
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