The footage, released late Monday, showed the man in an orange jumpsuit and blindfolded, kneeling in front of a group of armed men in the eastern city of Benghazi.
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As one of the men finishes reading out the sentence to "death for espionage," another one shoots him in the head several times to shouts of Allahu akbar (God is greatest).
The man was said to be a 39-year-old baker living in Benghazi, cradle of the 2011 revolution that ousted dictator Moamer Kadhafi and plunged the country into chaos that continues to the present.
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The North African nation has two rival governments and several armed groups vying for control of the country and its oil wealth, and Islamist extremists have exploited the turmoil to establish a foothold.
Two Tunisian journalists, Sofiene Churab and Nadhir Ktari, disappeared in Libya a year ago. IS announced in January that it had executed them, but the foreign ministry in Tunis recently said it had "irrefutable proof" they are still alive.
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