# Unraveling Geometry Problem 857: Exploring Triangles, Median, Midpoint, and Congruence with Auxiliary Lines - Mastering 30 and 45 Degree Angles

 Given triangle ABC with angle BAC = 30 degrees and angle ACB = 105 degrees, find the measure of angle ABD, where BD is the median from vertex B. Use only elementary geometry to solve this problem; do not use trigonometry. See More Geometry Problems: Geometry Problem 858 Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence, Angles, Auxiliary Lines. Geometry Problem 856 Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines. Geometry Problem 855 Quadrilateral, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines. Geometry Problem 854 Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines.
 Home | Search | Geometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 851-860 | Triangles | Midpoint | Median | Congruence | Angles | 30 degrees | 45 degrees | Email | Solution / comment | by Antonio Gutierrez