Given a triangle ABC, let BD be the median such that angles A and DBC are equal. If angle ADB measures 45 degrees, find the measure of angle A. Please use elementary geometry, such as Euclid's Elements. 

Geometry Problem 1

In triangle ABC, seek the unknown angle A,
With BD median and equal angles to weigh,
ADB at 45 degrees, a clue on display,
Use Euclid's Elements to solve the geometry today.

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.