完整的句子是不是 Many have different opinions about the extent to which greenhouse gases are responsible for it.
翻译：许多人对
温室气体负责程度有不同的看法。
the extent to which greenhouse gases are responsible for it.
这不是一个完整的句子，而是一个
名词性短语：the extent（程度），后面的to which...是一个
定语从句，修饰这个extent。 所以，这个名词性短语应该按”
先行词+定语从句”的 结构断为 the extent / to which greenhouse gases are responsible for it.
意思是：温室气体（在哪方面的）负责程度 ( 在哪方面，看it在上下文中指什么东西）
其他从网上找到的例子，帮助更好的理解：
先行词是the extent，后跟 to which的例句：
No one can forecast the extent to which traffic will grow.
没有人能预测将来交通流量会增长到什么程度。
She didn't realize the extent to which she had been distracted.
她没有意识到她心烦意乱的程度。
The extent to which the Court will modify these doctrines is, as yet, unclear.
法院对这些原则修正的范围现在尚不清楚。
The extent to which women have lost their rights in Iraq is shocking.
伊拉克妇女丧失权力的程度令人震惊。