noun
look of amazement; dumbfounded expression
Describes a facial expression showing disbelief, astonishment, or exasperation, often in reaction to something unexpected or foolish.
彼の言い訳に、彼女は呆れ顔を見せた。
She gave him a look of amazement at his excuse.
あまりの間違いに、先生は呆れ顔でため息をついた。
At the sheer number of mistakes, the teacher sighed with a dumbfounded expression.
The verb meaning 'to be amazed' or 'to be dumbfounded'; 呆れ顔 is the noun form describing the facial expression resulting from that feeling.
Compound of 呆れ (continuative form of 呆れる, 'to be amazed') + 顔 ('face').