Quadrilateral angle sums and special-quadrilateral properties

\(\square JKLM\) models an artwork border

The four angles are interior angles of the quadrilateral

Interior angle \(\angle J\): unknown

Interior angle \(\angle K\): \(38^\circ\)

Interior angle \(\angle L\): \(127^\circ\)

Interior angle \(\angle M\): \(105^\circ\)