Arch-?

Quick one:

archangel = ahrk-eyn-juhl
archenemy = ahrch-en-uh-mee

/k/ VS /ch/ = why, being as they're both before vowel sounds?

I'm thinking that it's to do with place of articulation of the /a/ and /e/ following them, or how the phonemes cluster into syllables ("chenemy", "kangel") but was wondering if anybody could give me a nice explanation. :D

Failing that, is/was 'archenemy' hyphenated/-able?