The figure shows a triangle ABC with altitudes AA', BB', and CC', where angle BAC measures 59 degrees. A line L passing through A' is parallel to B'C' and intersects the extension of AB at point D and the side AC at point E. The extensions of B'C' and CB intersect at point F. The circumcircle of triangle DEF intersects BC at point H. Find the measure of angle B'HC'.
