关于each独立主格的一道题

lvning

GWD-10-Q3

Forprotection from the summer sun, the Mojave lived in open-sided, flat-toppeddwellings known as shades, each a roof of poles and arrow weed supported by posts setin 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

答案是A,  我知道是each的独立主格，each应该是指代shades，但是总觉得each和a roof 之间少了with，或者否可以理解为has 省略，也就是谓语动词省略，构成独立主格？不能确定！请帮忙分析下A选项的结构。 先谢了！