This is an irregular verb. It follows the conjugation pattern of the verb chegar.
This verb is more common in European Portuguese. In Brazilian Portuguese, expressions like ficar bravo or ficar irritado are more commonly used.
Present:
A Ana zanga-se quando as pessoas mentem.
Ana gets angry when people lie.
Preterite:
O Miguel zangou-se com essa situação.
Miguel got angry about that situation.
Conditional:
A Clara zangar-se-ia se isso acontecesse.
Clara would get angry if that happened.