4. As shown in Figure 1, let $\triangle A B C$ and $\triangle C D E$ both be equilateral triangles, and $\angle E B D=62^{\circ}$. Then the degree measure of $\angle A E B$ is ( ).
(A) $124^{\circ}$
(B) $122^{\circ}$
(C) $120^{\circ}$
(D) $118^{\circ}$
4. B.

Obviously, $\triangle B C D \cong \triangle A C E$, so $\angle D C B=\angle E C A$.
Let $\angle B A E=\alpha$. Then
$\angle C B D=\angle C A E=60^{\circ}-\alpha$,
$\angle E B C=\angle E B D-\angle C B D=2^{\circ}+\alpha$.
Thus, $\angle E B A=60^{\circ}-\left(2^{\circ}+\alpha\right)=58^{\circ}-\alpha$.
Therefore, $\angle A E B=180^{\circ}-\alpha-\left(58^{\circ}-\alpha\right)=122^{\circ}$.