Who was theodora? protest leader in the nika rebellion roman mosaic artist architect of the hagia sophia empress of the byzantine empire

Hello!

Theodora was an empress, whose husband was the Emperor of the Byzantine Empire.
That makes answer D. [Empress of the Byzantine Empire] an unlogical answer since she only helped advance the Empire alongside her husband. 

Answer B. [Roman mosaic artist] is also incorrect. 
It was said that for a time, she made her living as a wool spinner. 
So, she did not have time to become an actual artist. 
This answer often is mistaken to be correct because she was represented in a mosaic portrait in the Church of San Vitale in Ravenna. 

Answer C. [Architect of the Hagia Sophia] is incorrect.
because it was directed under the direction of the Byzantine emperor Justinian I, her husband.

Your correct answer is A. [Protest leader in the Nika Rebellion]

Hope this helps!

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