In the diagram below, lines \(k\) and \(\ell\) are parallel. Triangle \(ABC\) is isosceles with \(AB = AC\). If \(\angle BAC = 40^\circ\) and \(\angle DBC = 70^\circ\), where \(D\) is a point on line \(\ell\) and \(BD\) intersects \(AC\) at \(E\), find the measure of \(\angle BEC\).

[asy]
size(200);
pair A = (1,2);
pair B = (0,0);
pair C = (2,0);
pair D = (3,0);
pair E = (1,0);
draw(A--B--C--cycle);
draw(B--D);
draw(A--C);
label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$D$", D, S);
label("$E$", E, S);
label("$k$", (3.5, 0));
label("$\ell$", (3.5, -0.5));
\end{asy} Let's think step by step and output the final answer within \boxed{}.
user