Problem 688: Triangle, Angles, 10, 20, 30, 40, 60 Degrees, Measure, Mind Map, Polya. Level: High School, College, SAT Prep.

The drawing shows a triangle ABC with points E and D on AB and AC, respectively. If the measure of the angles BAC, ACE, BCE, and ABD are 20, 30, 10, and 60 degrees, respectively, find the measure of angle BDE.
 

 
 

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."

George Pólya's 1945 book "How to Solve It, A new aspect of Mathematical Method", is a book describing methods of problem solving. It suggests the following steps when solving a mathematical problem: (1) First, you have to understand the problem. (2) After understanding, then make a plan. (3) Carry out the plan. (4) Look back on your work. How could it be better?