a little angry: miffed informal, peeved informal
rather angry: annoyed, irritated, cross, in a bad/foul
mood
very angry: furious, livid, outraged, incensed, incandescent with rage formal
to become angry: lose your temper, go mad British English, go berserk informal, go ballistic informal, hit the roof informal
words for describing someone who often gets angry: bad-tempered, grouchy, cantankerous, crabby, stroppy BrE informal