[求助]语法 一道

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

with roofs of poles and arrowweed that are

答案是原题中的划线部分，请大家解释一下为什么with 不行好吗？

each a roof of poles and arrowweed 是个（不定代词+名词）独立主格。

这个with+名词短语不知道做什么成分。