Puzzles like this one not half making you angry (5)
I believe the answer is:
cross
'angry' is the definition.
(I've seen this before)
'puzzles like this one not half' is the wordplay.
'puzzles like this one' becomes 'crosswords' (the puzzle you are doing is a crossword).
'not half' indicates taking half.
'crosswords' halved is 'CROSS'.
'making you' is the link.
(Other definitions for cross that I've seen before include "Crucifix" , "Peeved" , "X" , "Thwart, oppose" , "Annoyed; symbol" .)