Sentence Correction

For protection from the summer sun, the Mojave lived in open-sided, flat-topped dwellings known as shades, each a roof of poles and arrowweed supported by posts set in a rectangle.
(A) each a roof of poles and arrowweed
(B) each a roof of poles and arrowweed that are being
(C) with each being a roof of poles and arrowweed
(D) with roofs of poles and arrowweed to be
(E) with roofs of poles and arrowweed that are


Official Answer: A

Please discuss.
Thanks,
iwill.