4. In $\triangle A B C$, $A B=A C=b, B C=a$. If $\frac{a}{b}=\frac{\sqrt{5}-1}{2}$, then $\triangle A B C$ is called a "golden triangle". In a golden $\triangle A B C$, the measure of $\angle A$ is ( ).
(A) $36^{\circ}$
(B) $54^{\circ}$
(C) $72^{\circ}$
(D) $108^{\circ}$