MathNet 2006 — Part 02 Question 33

Let $ABCD$ be a convex quadrilateral such that $AB = AD$ and $CB = CD$. Angle bisector $\widehat{BDC}$ cuts $BC$ at $L$, and $AL$ cuts $BD$ at $M$. It is known that $BL = BM$.
Determine the value of $2\widehat{A} + 3\widehat{C}$.