Question 51
In triangle $ABC$, $AB = 2$, $AC = 1 + \sqrt{5}$, and $\angle CAB = 54^{\circ}$. Suppose $D$ lies on the extension of $AC$ through $C$ such that $CD = \sqrt{5} - 1$. If $M$ is the midpoint of $BD$, determine the measure of $\angle ACM$, in degrees.