Answer
$m\angle K=79^{\circ}$
Work Step by Step
Since the two quadrilaterals are similar, the corresponding angles are congruent. So...
$m\angle H=m\angle A=55^{\circ}$
$m\angle J=128^{\circ}$
$m\angle D=m\angle L=98^{\circ}$
The four interior angles of a quadrilateral sum to $360^{\circ}$.
$360-55-128-98=79$
$m\angle K=79^{\circ}$
