Why are the endings to these two words pronounced differently? Mangia ~ Genealogia

The puzzle is easily solved: there is no “i” sound in mangia, it is just a graphic device for denoting the palatal pronunciation of “g”, like in gelato. So, apart from the different vowel following it, the sound is the same /ʤ/.

It's the same for “c”: the palatal pronunciation is denoted by inserting an “i” before “a”, ”o” or “u”: goccia (drop), gancio (hook), ciuco (donkey).

To the contrary, the “hard” sound is denoted by inserting an “h” before “e” and “i”: che (conjunction or pronoun), chi (who), alghe (seeweed), ghiro (dormouse).

So the verb mangiare has no “i” in its root; indeed the future tense is mangerò, mangerai, because there's no need to denote the palatal pronunciation.

Sometimes, however, for etymological reasons (but the real reason is some imposition by grammarians), the “i” is preserved; it's the case of plurals, so camicia (shirt) becomes camicie and ciliegia (cherry) becomes ciliegie. In both cases the “i” still has no sound.

The case of cielo (sky) and cieco (blind) is a bit different: ancient Italian (Tuscan) pronounced this “i”; it's still heard in southern Italian speakers.

In some words, though, the “i” sound is present and it is tonic, like farmacia (apothecary) or genealogia. Of course, in this case, it is pronounced with palatal sound.

A curious case are the adverbs già and giù where there is no diphthong (/ʤa/ and /ʤu/), but they're written with an accent in analogy with più.

Pronunciation of -gia and -cia is a bit tricky, however in this case 'genealogia' derives from Greek, so it is pronounced -gì-a.

As other users have already pointed out, the difference here is in the position of the stress: genealogia: [ge-ne-a-lo-gì-a] vs. mangiare: [man-già-re] (mangiare is the infinitive tense of the word mangia).

If you have a doubt about a word pronunciation, you can look it up in a phonetic dictionary such as Dipi (and if you are lucky enough you may even find it! ?) and look at the phonetic transcription of your word or of a similar word. For example, you'll find genealogia (/ʤenealoˈʤia/), but you won't find mangia or mangiare; anyway, if you type mangia in the research bar, you'll get similar words, such as Torre del Mangia (/ˈtorre delˈmanʤa/) and deduce that the pronunciation of mangia is /manʤa/. However, this is a very fortuitous situation...

A very useful tool for Italian language learners is Forvo, a website filled with the pronunciation of hundreds of words by native Italian language speakers. Here I've found both the pronunciation of genealogia and the pronunciation of mangia.