na-adjective
looking comfortable; seeming at ease
Describes someone's appearance or manner as appearing comfortable, content, or in a good mood. Often used with 様子, 顔, or 表情.
彼女は心地よげにソファに座っていた。
She was sitting on the sofa looking comfortable.
猫が日向で心地よげに眠っている。
The cat is sleeping comfortably in the sun.
心地よい is an i-adjective meaning 'comfortable' (describing a thing or experience), while 心地よげ is a na-adjective describing someone's appearance of comfort.
Compound of 心地 (ここち, 'feeling, comfort') + よげ, the stem of よい ('good') with the suffix げ ('seeming, appearing').