chin
頦 centers on the chin, the lower front part of the face.
頦 combines 亥 (likely a phonetic component) with 頁 (head), pointing to a part of the head. The exact historical development is uncertain.
The right side 頁 means head or page, and the left side 亥 looks like a jawline. Picture the head with the chin area highlighted: 頦 is the chin.
For カイ, imagine a chin so sharp it could cut like a knife: knife -> カイ, and the chin is the cutting edge of the face.