The alphabet letter combination ea makes 6 sounds: bread [bred], teacher ['tiːʧə], break [breɪk], idea [aɪ'dɪə], pageant ['pæʤənt], bearable ['beərəbl].
I know that that the fact that the same letter combination can be read in so many different ways is related to the history of the English language. And basically it's easier to consult a dictionary and just remember the correct way of reading.
But still why can ea be read in 6 different ways?
In the words "idea" and "pageant", the "ea" shouldn't be analyzed as the same digraph that occurs in the other words that you mention.
The pronunciation [aɪ'dɪə] came to have the sound [ɪə] via "smoothing" of "long e" sound followed by a schwa [ə] (the letter "a" regularly corresponds to schwa in word-final position, when the vowel is unstressed).
In the pronunciation ['pædʒənt], the [ə] sound should be thought of as corresponding to the letter "a" only. The letter "e" is silent, and can be grouped with the preceding [ʤ] sound. When the letter "e" or "i" occurs after a consonant letter and before another vowel letter, and does not represent a stressed vowel, it may represent:
No sound at all:
if the preceding sound is [dʒ] [tʃ], [ʒ] or [ʃ]: e.g. ocean, righteous, courageous, some pronunciations of nausea (some words with [dʒ] [tʃ], [ʒ] or [ʃ] before "e" have two pronunciations: one where the "e" is silent and one where it is pronounced as the "happy" vowel /i/)
in some cases, an "e" before a vowel letter is silent after a consonant sound that is not in the list above if the word is related to a shorter word ending in "silent e": e.g. sizeable. But this word has the variant spelling sizable. Also, this criterion doesn't always give you the right pronunciation: the e in "phraseology" is not silent, even though the related word "phrase" ends in a "silent e".
Note that in some words, a "silent" letter "e" occurs just to indicate that a preceding letter "g" is pronounced as [dʒ] rather than as [g]: for example, words ending in "geable" such as manageable, changeable. These words must be spelled with "silent e", unlike sizeable.
That leaves us with 4 cases to explain of words that are truly spelled with the "ea" digraph.
teacher. The word "teacher" has the "expected" value for "ea": the "long e" sound /iː/. In most words spelled with "ea", this developed from Middle English /ɛː/ via a regular sound change (part of what is called the "Great Vowel Shift", which changed the pronunciation of long vowels between Middle English and Old English).
bread. This word shows a sporadic but fairly common change: Middle English /ɛː/ was shortened to /ɛ/ and so did not develop according to the "Great Vowel Shift".
break. This word shows a very irregular development of Middle English /ɛː/. There are only a couple of other words that show the same change of Middle English /ɛː/ to present-day English /eɪ/: great and steak.
bear(able). The pronunciation of bearable is just based on the pronunciation of the root verb bear. In this word, the Middle English vowel /ɛː/ ended up developing to /eə/ (the r-controlled "long a" sound), partly due to the influence of the following "r". But in other words such as "fear" we see the r-controlled "long e" sound instead ([ɪə(r)]), so the pronunciation of the trigraph "ear" is somewhat unpredictable. A rule of thumb that might be useful is that if a verb has an irregular past-tense form with the /ɔː(r)/ sound, and a present-tense form spelled with "ear", then you can expect that it will be pronounced with /eə(r)/ in the present tense.
You can see a more detailed discussion of break, great and steak in my answer to the following ELU question: Why is “great” pronounced as “grate”, but spelled with “ea”?
