In triangle ABC, ∠ABC=30∘,∠ACB=60∘. D is a point in triangle ABC such that DB and DC bisect angles ABC and ACB respectively. What is the measure (in degrees) of ∠BDC?

Answer 1

Consider the sum of the angles in triangle BDC. The two acute angles of that triangle are 60/2 and 30/2.

�ÚBDC is the remaining obtuse angle.

�ÚBDC = 180 - (15 + 30) = 135 ∘