11. In a convex hexagon $A B C D E F$ with 6 equal sides, the interior angles $A, B, C$ are $134^{\circ}, 106^{\circ}, 134^{\circ}$, respectively. Then the interior angle $E$ is $\qquad$
(Answer in degrees)
Rong's $134^{\circ}$.
Analysis Let the side length be 1, and let the midpoints of $A C$ and $D F$ be $M$ and $N$, respectively, and the projection of $A$ on $D F$ be $K$. Then
$$
\angle B A M=37^{\circ}, \angle M A F=97^{\circ}, \angle A F K=83^{\circ}
$$

That is,
$$
F K=\cos 83^{\circ}, \quad K N=A M=\cos 37^{\circ}
$$

Let $\angle E F N=x$, then $F N=\cos x$. Using $F N=F K+K N$, we have
$$
\cos x=\cos 83^{\circ}+\cos 37^{\circ}=2 \cos 60^{\circ} \cos 23^{\circ}=\cos 23^{\circ}
$$

Therefore, $x=23^{\circ}$, which means the base angle of isosceles $\triangle D E F$ is $23^{\circ}$. Thus, its vertex angle $E$ is $134^{\circ}$.