Problem D

The Angle Isn't Bad

Ewan drew rhombus \(ABCD\). Recall that a rhombus is a quadrilateral with parallel opposite sides, and all four sides of equal length. In Ewanâ€™s rhombus, \(H\) is on \(BC\) in between \(B\) and \(C\), and \(K\) is on \(CD\) in between \(C\) and \(D\), such that \(AB=AH=HK=KA\).

Determine the measure, in degrees, of \(\angle BAD\).