How to associate median with angles?? I have got an olympiad problem which is like follow: In triangle ABC,let D be the midpoint of BC.If ∠ADB=45 and ∠ACD=30 ,determine ∠BAD. The main problem with the question is that the given things are two angles and a median.I don't know how to relate these two (Appolonius's theorem won't work). Any suggestion is heartily welcome.

Hint: note that $\widehat{CAD} = 15^\circ $ and $\widehat{ABD} + \widehat{BAD} = 135^\circ$. Apply the sine law twice to get:

$$\frac{AD}{CD} = \frac{\sin 30^\circ}{\sin 15^\circ} = \frac{\sin(135^\circ -\widehat{BAD})}{\sin \widehat{BAD}} $$