My boss is angry at me

Can anyone please explain why option "A" is correct and not option "B"?

It may come out as if I'm defending the answer, but how I approached this question right now, just before writing this, is:

with preposition is used to denote association and GMAT strictly follow such regulations when it comes to prepositions.
The boss is angry with me may also mean that: Both boss and I are angry because someone else lied.

While angry at is idiomatic. Sorry, you've to memorize them like laughing at someone

That was my learning while going through OG: use prepositions in their crude sense. And I've never found any exception while going through OG, OG Verbal Guidee Review, MGMAT SC strategy guide and GMAT Club practice questions.
So, I would suggest - use prepositions only in crude sense, sans idioms.
Hope it helps.

Cheers

You may not be correct at that. The idioms do not follow any rationale.
You will find plenty of official questions using 'with' in a way that does not adhere to above assumption.

For example..
673. While Noble Sissle may be best known for his
collaboration with Eubie Blake, as both a vaudeville
performer and as a lyricist for songs and Broadway
musicals, also enjoying an independent career as a
singer with such groups as Hahn’s Jubilee Singers.

Similarly you will find other idioms, such as agree with, contrast with, not following the literal meaning of WITH as written in your post.
He agrees with you.
I went to the market with him.

egmat generis GMATNinja Can anyone please tell that why option D is wrong?

D. My boss is angry on me for lying.

This option is wrong for the simple reason that using "on" with "is angry" is unidiomatic.

The convention is to use "at" or "with" with "is angry."

Hi,
Then why we chose Option A over option B?
Please help me to understand this !