The antique prefix arch- comes up in words like arch-nemesis, archenemy, archbishop etc. It means something like “highest” or “supreme”.

✔️ In all these words it’s pronounced with a “ch” sound (like in cheese).

💡 IPA: /ɑɹt͡ʃ/

Audio on Forvo: https://forvo.com/word/arch-nemesis/#en

Unrelated in meaning, but pronounced also with a “ch”, is the word arch and its derivatives like overarching. Forvo

Words that are pronounced with “k”

However, more often than not, “ch” in words of Ancient Greek origin is pronounced like “k”: e.g. architecture, archeology, archaic, Plutarch, monarchy.

But not the arch prefix! That one is always pronounced “ch”.

Arch photo by Ulvi Safari on Unsplash