Margrethe II ( Margrethe Alexandrine Ã Ã rhildur Ingrid ) ( born 16 April 1940 ) is the Queen regnant of Denmark . Margrethe II ( Margrethe Alexandrine Ã Ã rhildur Ingrid , sometimes anglicised as Margaret II ) ( born 16 April 1940 ) is the queen regnant of Denmark .