The following is from one of the definitions of a word in goo辞書:
I do not understand why か is used here instead of こと.
Usually, I would expect to see の (or こと) nominalize a verb. Nonetheless, I reckon it would be ungrammatical here, since what follows is the possessive の, and a noun (度合い).
Alternatively, if I were to write this phrase myself, I would simply attach the plain verb (傾く) to the noun (度合い):
Which seems to express the same thing to me.
I do not think this かの is かのように, but what about 彼の? If I understand correctly, 彼の is simply an old-fashioned way of saying あの. If so, the phrase could be rewritten thus:
Which seems strange to me. (I am a low-level beginner though.) Could someone please help me understand the grammar at work here?