MHB Find Measure of ∠BAD in ABCD Rhombus

[Ilikebugs]

A parallelogram is a quadrilateral with opposite sides parallel. A rhombus is a parallelogram with all four sides having equal length.

ABCD is a rhombus. H is on BC, between B and C, and K is on CD, between
C and D, such that AB = AH = HK = KA.
Determine the measure of ∠BAD.I've tried making isosceles triangles with little success

 

[Evgeny.Makarov]

\begin{tikzpicture}
\renewcommand\ss{2}
\coordinate[label=above:$A$] (A) at (0,0);
\path (A) ++(220:\ss) coordinate[label=left:$D$] (D);
\path (A) ++(-40:\ss) coordinate[label=right:$B$] (B);
\path (D) ++(-40:\ss) coordinate[label=below:$C$] (C);
\path (A) ++(-60:\ss) coordinate[label=below right:$H$] (H);
\path (A) ++(240:\ss) coordinate[label=below left:$K$] (K);
\draw (A) -- (B) -- (C) -- (D) -- cycle;
\draw (A) -- (H) -- (K) -- cycle;
\foreach \p in {A,B,D,C,H,K} \fill (\p) circle (1.5pt);
\end{tikzpicture}​

I suggest denoting $\angle B=\angle D$ by $x$ and trying to express other angles through it, eventually arriving at some equation in $x$. Note that the sides of the rhombus and the sides of the triangle are all equal.

 

[Ilikebugs]

I got A=100 degrees?

 

[Greg]

$x=\angle{B},\quad2x+4(180-2x)+120=360\implies x=80^{\circ}\implies\angle{BAD}=100^{\circ}$