In a triangle ABC, the median BD is such that the angles A and DBC are equal. If the measure of the angle ADB is 45 degrees, find the measure of angle A. Try to use elementary geometry (Euclid's Elements.)
 

See solution below

See also:
Triangles
Median
Congruence
Circle
Geometric Art 01
Stereographic projection of Machu Picchu
Kaleidoscope of Geometry Problem 1 based on Poincare Disk Model 

Poster and Typography of problem 1

Geometric Art of problem 1

Mind Map: George Pólya's 1945 book, "How to Solve It"

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?
A mind map is a diagram used to visually organize information, knowledge, concepts or ideas.