Buddhism speaks of the three poisons: greed, anger, and delusion.
Tips
culture
In Buddhism 嗔 is one of the 三毒 (the three poisons): 贪 (greed) 嗔 (anger) 痴 (delusion) - the root causes of suffering. Knowing this term is key for reading Buddhist or Journey-to-the-West passages.
memory
Mouth radical 口 + 真 (zhēn, true) - phonosemantic: anger spoken from the mouth, with 真 hinting at the pinyin chēn.
Left mouth radical anchors 嗔 in the speech/sound family - here a sharp angry voice. The mouth radical commonly indexes verbs of utterance (吼 roar, 骂 scold, 喊 shout) and the angry/scolding semantic flavour fits 嗔 precisely.
Right 真 supplies the sound - zhēn drifting to chēn with the regular zh/ch alternation. Same phonetic appears in 慎 cautious, 镇 town, 颠 topple, 填 fill. 真 contributes no transparent meaning here; the angry-utterance sense comes wholly from the mouth radical and historical use.