na-adjective
thoughtful; pensive; speculative
Describes a person's appearance or manner as looking deeply thoughtful or contemplative. Often used with 様子, 顔, or 表情. Related to 考え深い (thoughtful, deep-thinking).
See also: 考え深い
彼は考え深げな様子で窓の外を見ていた。
He was looking out the window with a thoughtful expression.
先生は考え深げにうなずいた。
The teacher nodded thoughtfully.
考え深い is an adjective meaning 'thoughtful' or 'deep-thinking' as a character trait, while 考え深げ describes the outward appearance of being thoughtful.
Formed from the adjective 考え深い (thoughtful) by replacing the final い with the suffix げ, which indicates an appearance or manner.